CBSE Class 5 Mathematics Lines Angles Circles Worksheet

Ln. 18 : Lines, Angles and Circles

1. Fill in the blanks :

Question 1.1. A ______________ is an exact location.
Answer: point
In simple words: A point gives us the exact position or location in space.

Exam Tip: Remember that a point has no length, breadth, or thickness; it only indicates position.

Question 1.2. A ______________ represents a point.
Answer: sharp tip of a pencil
In simple words: A dot made by a sharp pencil tip represents a geometric point.

Exam Tip: Always associate a dot with a point in geometry.

Question 1.3. The straight path between two points is called the ________________ .
Answer: line segment
In simple words: The shortest straight distance connecting two fixed points is a line segment.

Exam Tip: A line segment has fixed endpoints, unlike a line.

Question 1.4. A line segment has ______________ end points.
Answer: two
In simple words: A line segment starts at one point and ends at another, making two endpoints.

Exam Tip: Two endpoints mean it has a measurable, finite length.

Question 1.5. The line segment has________________ length.
Answer: definite (or fixed)
In simple words: You can measure a line segment with a ruler because it has a fixed length.

Question 1.6. A line segment extended endlessly in one direction is called a ________________.
Answer: ray
In simple words: A ray starts at one endpoint and goes on forever in a single direction.

Exam Tip: Think of a sunbeam starting at the sun and traveling infinitely into space.

Question 1.7. ________________ has one end point.
Answer: A ray
In simple words: A ray has a starting point but no ending point.

Exam Tip: One endpoint distinguishes rays from lines (zero endpoints) and line segments (two endpoints).

Question 1.8. A line segment extended endlessly on both sides is called a ________________.
Answer: line
In simple words: A straight path that goes on forever in both directions is a line.

Exam Tip: Lines cannot be measured completely because they have infinite length.

Question 1.9. ________________ has no end points.
Answer: A line
In simple words: A line extends infinitely on both sides, so it has no endpoints.

Exam Tip: Arrowheads on both ends of a drawing indicate that the line goes on forever.

Question 1.10. ________________ does not have a definite length.
Answer: A line (or a ray)
In simple words: Since lines and rays extend endlessly, they do not have a fixed, measurable length.

Exam Tip: Only line segments have a definite length.

Question 1.11. Two rays having a common endpoint they form an _____________.
Answer: angle
In simple words: When two rays start from the exact same point, they create an angle.

Exam Tip: The opening between the two rays is the measure of the angle.

Question 1.12. The common endpoint is called the________________ of an angle.
Answer: vertex
In simple words: The corner point where two rays meet is called the vertex.

Exam Tip: When naming an angle, the vertex letter must always be written in the middle.

Question 1.13. A line segment is part of a ________________.
Answer: line
In simple words: A line segment is just a finite piece taken out of a full line.

Exam Tip: Every line segment lies on some underlying straight line.

Question 1.14. The unit of measurement of an angle is ________________.
Answer: degree (\(^\circ\))
In simple words: Angles are measured in degrees using a protractor.

Exam Tip: Always write the small circle symbol (\(^\circ\)) after the number when stating an angle measure.

Question 1.15. Angle that is equal to \(90^\circ\) is called ________________ angle.
Answer: right
In simple words: A square corner measures exactly \(90^\circ\) and is called a right angle.

Exam Tip: Right angles are often marked with a small square at the vertex.

Question 1.16. Angle that is greater than a right angle is called ________________ angle.
Answer: obtuse
In simple words: An angle wider than a right angle (\(90^\circ\)) but less than a straight angle (\(180^\circ\)) is an obtuse angle.

Question 1.17. Angle that is greater than \(0^\circ\) and less than a right angle is called ________________ angle.
Answer: acute
In simple words: An angle smaller than \(90^\circ\) is an acute angle.

Exam Tip: Think of acute as "sharp and small".

Question 1.18. Angle that is greater than \(180^\circ\) but less than \(360^\circ\) is called ________________ angle.
Answer: reflex
In simple words: A reflex angle bends back further than a straight line, measuring between \(180^\circ\) and \(360^\circ\).

Exam Tip: Always look at which side of the vertex is being measured when dealing with reflex angles.

Question 1.19. Angle that is equal to \(360^\circ\) is called ________________ angle.
Answer: complete (or full turn)
In simple words: A full rotation around a point makes a complete angle of \(360^\circ\).

Exam Tip: A complete angle brings you right back to where you started.

Question 1.20. An obtuse angle is always ______________ \(90^\circ\).
Answer: greater than
In simple words: Obtuse angles always measure more than \(90^\circ\).

Exam Tip: Range for obtuse angle is \(90^\circ < \text{Angle} < 180^\circ\).

Question 1.21. An Acute angle is more than _____________ but less than _____________.
Answer: \(0^\circ\), \(90^\circ$
In simple words: Acute angles lie strictly between \(0^\circ\) and \(90^\circ\).

Exam Tip: An angle of exactly \(0^\circ\) or \(90^\circ\) is neither acute.

Question 1.22. The straight angle is equal to two _______________ angles.
Answer: right
In simple words: Two right angles (\(90^\circ + 90^\circ\)) make a straight angle (\(180^\circ\)).

Question 1.23. The straight angle measures exactly _______________.
Answer: \(180^\circ$
In simple words: A straight line forms an angle of \(180^\circ\).

Exam Tip: A straight angle looks like a flat line.

Question 1.24. _______________ angle measures exactly \(360^\circ\).
Answer: Complete (or Full turn)
In simple words: A full circle turn is \(360^\circ\).

Exam Tip: Useful in geometry for analyzing total angles around a point.

Question 1.25. A right angle is equal to _______________.
Answer: \(90^\circ$
In simple words: A right angle is always \(90^\circ\).

Exam Tip: Fundamental benchmark for all angle classifications.

Question 1.26. The parts of an angle are _______________ and _______________.
Answer: two arms (or rays), vertex
In simple words: An angle consists of a vertex and two arms.

Exam Tip: Never forget both structural components.

Question 1.27. An angle that measure \(1^\circ\) is an_______________ angle.
Answer: acute
In simple words: Since \(1^\circ\) is less than \(90^\circ\), it is acute.

Question 1.28. SR and ST are called the _______________.
Answer: arms of the angle
In simple words: In the reference diagram, rays SR and ST form the two arms of angle RST.

Exam Tip: Rays forming an angle originate from the vertex S.

Question 1.29. The angle alongside is called ______________ .
Answer: Angle RST (or \(\angle RST\))
In simple words: The angle formed by rays SR and ST with vertex S is named \(\angle RST\).

Exam Tip: Read the letters systematically along the rays through the vertex.

Question 1.30. Angle RST is written as ______________.
Answer: \(\angle RST$
In simple words: The mathematical symbol for angle is \(\angle\).

Question 1.31. The middle letter is always the ______________ of the angle.
Answer: vertex
In simple words: In three-letter angle names like \(\angle RST\), the middle letter S represents the vertex.

Exam Tip: This is a foolproof rule for naming angles.

Question 1.32. The angle is measured by a ______________.
Answer: protractor
In simple words: A D-shaped instrument called a protractor is used to measure angles.

Question 1.33. The protractors have scale ______________ to ______________.
Answer: \(0^\circ\), \(180^\circ$
In simple words: A standard protractor has inner and outer scales running from \(0^\circ\) to \(180^\circ\).

Exam Tip: Use the inner scale if the angle opens to the right, and the outer scale if it opens to the left.

Question 1.34. A line segment joining two points on the circle called ______________ of the circle.
Answer: chord
In simple words: Any line segment connecting two distinct points on a circle's boundary is a chord.

Exam Tip: The diameter is the longest possible chord in a circle.

Question 1.35. The distance around a circle is called the ______________.
Answer: circumference
In simple words: Circumference is the perimeter or total boundary length of a circle.

Question 1.37. All the radii of a circle are ______________.
Answer: equal in length
In simple words: Every radius from the center to any point on the circle has the exact same length.

Exam Tip: Radius is constant for a given circle.

Question 1.38. A line segment joining two points on the circle and passing through the centre is called _____________ of the circle.
Answer: diameter
In simple words: A chord that passes directly through the center point is the diameter.

Exam Tip: Diameter divides the circle into two equal semicircles.

Question 1.39. The diameter of a circle is the ______________ chord of the circle.
Answer: longest
In simple words: No chord in a circle can be longer than its diameter.

Exam Tip: Diameter = \(2 \times \text{Radius}\).

Question 1.40. Diameter is ______________ of the radius.
Answer: twice (or double)
In simple words: The diameter is two times as long as the radius.

Exam Tip: \(d = 2r\).

Question 1.41. Radius is ______________ of the diameter.
Answer: half
In simple words: The radius is exactly half the length of the diameter.

Exam Tip: \(r = \frac{d}{2}\).

Question 1.42. All the diameters of a circle are ______________.
Answer: equal in length
In simple words: Every diameter passing through the center has the same measurement.

Exam Tip: All diameters equal \(2r\).

Question 1.43. The region inside a circle is called the ______________ of the circle.
Answer: interior
In simple words: The area enclosed within the circular boundary is the interior.

Exam Tip: Points inside the circle are at a distance less than the radius from the center.

Question 1.44. The region outside a circle is called ______________ of the circle.
Answer: exterior
In simple words: Everything outside the circular boundary is the exterior.

Exam Tip: Points in the exterior lie at a distance greater than the radius from the center.

2. Classify the angles whose measures are given below

Question 2.i) \(89^\circ$
Answer: Acute angle
In simple words: Since \(89^\circ\) is less than \(90^\circ\), it is acute.

Exam Tip: Just \(1^\circ\) less than a right angle is still acute.

Question 2.ii) \(91^\circ$
Answer: Obtuse angle
In simple words: Since \(91^\circ\) is greater than \(90^\circ\), it is obtuse.

Exam Tip: Even slightly exceeding \(90^\circ\) makes an angle obtuse.

Question 2.iii) \(12^\circ$
Answer: Acute angle
In simple words: \(12^\circ\) is much smaller than \(90^\circ\), so it is acute.

Exam Tip: Sharp, narrow angles are acute.

Question 2.iv) \(179^\circ$
Answer: Obtuse angle
In simple words: \(179^\circ\) is just under \(180^\circ\), making it obtuse.

Exam Tip: Do not confuse it with a straight angle (\(180^\circ\)).

Question 2.v) \(90^\circ$
Answer: Right angle
In simple words: Exactly \(90^\circ\) is a right angle.

Exam Tip: Right angles form perpendicular lines.

Question 2.vi) \(200^\circ$
Answer: Reflex angle
In simple words: Since \(200^\circ\) is greater than \(180^\circ\) and less than \(360^\circ\), it is a reflex angle.

Question 2.vii) \(180^\circ$
Answer: Straight angle
In simple words: Exactly \(180^\circ\) forms a straight line.

Exam Tip: A straight angle is equal to two right angles.

Question 2.viii) \(360^\circ$
Answer: Complete angle (Full turn)
In simple words: A full circle rotation is \(360^\circ\).

Exam Tip: Represents a full revolution around a point.

3. Construct the following angles with the help of a protractor.

Question 3.i. \(60^\circ$
Answer:
1. Draw a base ray with endpoint (vertex) at the left.
2. Place the protractor center on the vertex and align the baseline with the ray.
3. Mark a point at \(60^\circ\) on the inner scale.
4. Draw a ray from the vertex through the marked point.
In simple words: Constructing an acute angle of \(60^\circ\).

Exam Tip: Equilateral triangles have \(60^\circ\) interior angles.

Question 3.ii. \(110^\circ$
Answer:
1. Draw a base ray pointing to the right.
2. Position the protractor center on the vertex.
3. Find \(110^\circ\) on the scale starting from \(0^\circ\) on the right and make a dot.
4. Connect the vertex through the dot to complete the obtuse angle.
In simple words: Constructing an obtuse angle measuring \(110^\circ\).

Exam Tip: Ensure you read the correct scale so the angle opens wide as required for an obtuse angle.

Question 3.iii. \(135^\circ$
Answer:
1. Draw a horizontal base ray.
2. Place the protractor center at the vertex.
3. Locate \(135^\circ\) (halfway between \(130^\circ\) and \(140^\circ\)) and mark a point.
4. Draw the second ray from the vertex through the point.
In simple words: Constructing an obtuse angle of \(135^\circ\).

Exam Tip: Double-check that \(135^\circ\) is greater than \(90^\circ\).

Question 3.iv. \(90^\circ$
Answer:
1. Draw a horizontal base ray.
2. Place the protractor center at the vertex.
3. Mark a point precisely at \(90^\circ$ vertically upright.
4. Draw a vertical line segment or ray from the vertex through the mark.
In simple words: Constructing a perpendicular right angle.

Exam Tip: A right angle forms an exact 'L' shape when oriented vertically and horizontally.

Question 3.v. \(175^\circ$
Answer:
1. Draw a base ray.
2. Center the protractor on the vertex.
3. Mark a point at \(175^\circ\), which is just \(5^\circ\) short of a straight line (\(180^\circ\)).
4. Connect the vertex to the point.
In simple words: Constructing a very wide obtuse angle of \(175^\circ\).

Exam Tip: It will look almost like a straight flat line, bending only slightly.

4. Find the diameter of the circle with radius

Question 4.i. 3.6 cm
Answer:
Radius (\(r\)) = 3.6 cm
Diameter (\(d\)) = \(2 \times r\)
\(d = 2 \times 3.6\text{ cm} = 7.2\text{ cm}\)
In simple words: Multiply the radius by 2 to get the diameter.

Exam Tip: Formula: \(d = 2r\).

Question 4.ii. 9.9 cm
Answer:
Radius (\(r\)) = 9.9 cm
Diameter (\(d\)) = \(2 \times 9.9\text{ cm} = 19.8\text{ cm}\)
In simple words: Double 9.9 cm to find 19.8 cm.

Exam Tip: Watch your decimal placement during multiplication.

Question 4.iii. 13 cm
Answer:
Radius (\(r\)) = 13 cm
Diameter (\(d\)) = \(2 \times 13\text{ cm} = 26\text{ cm}\)
In simple words: Double 13 to get 26 cm.

Exam Tip: Always include units (cm) in your final answer.

5. Find the radius of the circle with diameter

Question 5.i. 9 cm
Answer:
Diameter (\(d\)) = 9 cm
Radius (\(r\)) = \(d \div 2\)
\(r = 9 \div 2 = 4.5\text{ cm}\)
In simple words: Divide the diameter by 2 to find the radius.

Exam Tip: Formula: \(r = \frac{d}{2}\).

Question 5.ii. 8.6 cm
Answer:
Diameter (\(d\)) = 8.6 cm
Radius (\(r\)) = \(8.6 \div 2 = 4.3\text{ cm}\)
In simple words: Half of 8.6 is 4.3 cm.

Exam Tip: Halve both the whole number and decimal parts.

Question 5.iii. 11.4 cm
Answer:
Diameter (\(d\)) = 11.4 cm
Radius (\(r\)) = \(11.4 \div 2 = 5.7\text{ cm}\)
In simple words: Half of 11.4 is 5.7 cm.

Exam Tip: Double-check by multiplying 5.7 by 2 to recover 11.4.

6. Draw the circles

Question 6.i. radius = 3.7 cm
Answer:
1. Set a compass to a radius of 3.7 cm using a ruler.
2. Fix the needle point on a paper sheet as the center.
3. Rotate the pencil smoothly around the center to draw the circle.
In simple words: Draw a circle with a compass opened to 3.7 cm.

Exam Tip: Keep the compass hinge tight so the radius doesn't slip while drawing.

Question 6.ii. Diameter = 11 cm
Answer:
1. First calculate the radius: \(11 \div 2 = 5.5\text{ cm}\).
2. Set your compass radius to 5.5 cm.
3. Draw the circle.
In simple words: Find the radius (5.5 cm) first, then draw the circle using a compass.

Exam Tip: Always convert diameter to radius before setting your compass.

Question 6.iii. radius = 2.5 cm and measure its longest chord
Answer:
1. Set compass to 2.5 cm and draw the circle.
2. Draw a diameter passing through the center.
3. Measure the diameter with a ruler: it will measure 5.0 cm.
In simple words: Draw a circle of radius 2.5 cm. Its longest chord (diameter) is 5.0 cm.

Exam Tip: The longest chord of a circle is always its diameter (\(2 \times 2.5\text{ cm} = 5.0\text{ cm}\)).

7. In the given figure name the following

Question 7.i) Centre of the circle
Answer: O
In simple words: Point O is the exact center of the circle.

Exam Tip: The center is equidistant from all points on the boundary.

Question 7.ii) All the radii
Answer: OE, OA, OC
In simple words: Line segments connecting the center O to points on the boundary (E, A, C) are radii.

Question 7.iii) All the diameters
Answer: EC (line segment passing through center O from E to C)
In simple words: EC is the chord passing through the center O, making it a diameter.

Exam Tip: Diameters must pass straight through the center.

Question 7.iv) All the chords
Answer: AD, EC (and any other line segments joining two points on the circle shown)
In simple words: Chords connect any two points on the circle's boundary.

Exam Tip: Every diameter is also a chord, but not every chord is a diameter.

Question 45. The diameter of a circle divides it into ______________ equal halves.
Answer: two
In simple words: A diameter splits a circle into two symmetrical semicircles.

Exam Tip: Each half is called a semicircle.

Question 46. Half of a circle is called ______________.
Answer: semicircle
In simple words: Exactly half of a circle's area and circumference is a semicircle.

Exam Tip: A semicircle measures \(180^\circ\) along its arc.

Question 47. A circle can be divided into 4 equal parts, each part is called ______________.
Answer: quadrant
In simple words: Dividing a circle into four equal quarters gives four quadrants.

Exam Tip: Each quadrant represents \(90^\circ$ (\(\frac{1}{4}\) of \(360^\circ\)).

Question 48. Quadrant is ______________ of a circle.
Answer: one-fourth (\(\frac{1}{4}\))
In simple words: A quadrant is equal to \(\frac{1}{4}\)th part of the whole circle.

Exam Tip: \(360^\circ \div 4 = 90^\circ\).

Question 49. Any part of the circumference of a circle is called the ______________.
Answer: arc
In simple words: A connected piece of the curved boundary of a circle is an arc.

Exam Tip: Arcs can be minor or major depending on their length.

Question 50. Half of the semicircle is called ______________.
Answer: quadrant
In simple words: Half of a semicircle (\(180^\circ \div 2 = 90^\circ\)) is a quadrant.

Exam Tip: Relates fractions of a circle directly to angle measures.

Question 51. All the chords of a circle are ______________.
Answer: less than or equal to the diameter
In simple words: No chord can exceed the length of the diameter.

Exam Tip: The diameter is the maximum possible length for a chord.

II. Answer the following questions.

1. Fill in the blanks with the help of the figure given here :

Question II.1.i. OC is a ______________
Answer: radius
In simple words: OC connects the center O to point C on the circle, so it is a radius.

Exam Tip: Center to boundary = radius.

Question II.1.ii. AB is a ______________
Answer: diameter (or chord passing through center)
In simple words: AB passes through the center, making it a diameter and chord.

Exam Tip: Longest chord in the circle.

Question II.1.iii. BD is a ______________
Answer: chord
In simple words: BD joins two points on the circle's boundary.

Exam Tip: Line segments joining circle points are chords.

Question II.1.iv. CD is a ______________
Answer: chord
In simple words: CD connects points C and D on the boundary.

Exam Tip: Any line segment between two boundary points is a chord.

Question II.1.v. OE is a ______________
Answer: radius
In simple words: OE runs from center O to point E on the circle.

Exam Tip: All radii in the same circle are equal.

Question II.1.vi. CAD is an ______________
Answer: arc (or triangle / angle depending on context, usually arc CAD or inscribed angle)
In simple words: CAD traces a curved section along the circle's boundary, representing an arc.

Exam Tip: Identified by points along the circumference.

Question II.1.vii. AB is double of ______________
Answer: radius (or OA, OC, OE)
In simple words: Diameter AB is twice the length of any radius.

Exam Tip: Diameter = \(2 \times \text{Radius}\).

Question II.1.viii. This circle has ___________ radii and ______________ chords
Answer: infinite (many), infinite (many)
In simple words: A circle can have countless radii and chords drawn in it.

Exam Tip: Circles are continuous curves with infinitely many possible line segments.

Question II.8) Measure the following angles and state the type of angle.
Answer:
1. Angle XYZ (top-left): Measures approx. \(120^\circ$ - Obtuse angle.
2. Angle PQR (top-right): Measures approx. \(45^\circ$ - Acute angle.
3. Angle ABC (bottom): Measures approx. \(60^\circ$ - Acute angle.
In simple words: Measure each angle using a protractor and classify based on its degree measure (\(<90^\circ\) acute, \(=90^\circ\) right, \(90^\circ - 180^\circ\) obtuse).

Exam Tip: Always align the protractor center with the vertex (Y, Q, and B respectively) for accurate readings.