CBSE Class 6 Mathematics Understanding Elementary Shapes Worksheet Set 05

I. Choose the correct option (Multiple Choice Questions) :

Question 1. Which type of triangle is this?
Triangle with length of sides 7 cm, 8 cm and 9 cm
(a) scalene triangle
(b) isosceles triangle
(c) equilateral triangle
(d) none of these
Answer: (a) scalene triangle
A triangle with all three sides of different lengths is called a scalene triangle. Here, sides are 7 cm, 8 cm, and 9 cm, which are all unequal.
In simple words: A triangle with different side lengths is a scalene triangle.

Exam Tip: Remember: Scalene = all sides unequal; Isosceles = two sides equal; Equilateral = all three sides equal.

Question 2. The cylinder has _______ bases.
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (b) 2
A cylinder has two identical flat circular bases, one at the top and one at the bottom.
In simple words: A cylinder has two circular bases.

Exam Tip: A cone has 1 base, a cylinder has 2 bases, and a sphere has 0 bases.

Question 3. The measure of a right angle is ______.
(a) \(60^\circ\)
(b) \(90^\circ\)
(c) \(30^\circ\)
(d) \(180^\circ\)
Answer: (b) \(90^\circ\)
An angle whose measure is exactly \(90^\circ\) is defined as a right angle.
In simple words: A right angle always measures \(90^\circ\).

Exam Tip: A right angle represents one quarter of a complete turn.

Question 4. An angle is ________ if its measure is smaller than that of a right angle.
(a) obtuse
(b) right
(c) straight
(d) acute
Answer: (d) acute
An angle smaller than a right angle (less than \(90^\circ\)) is called an acute angle.
In simple words: Angles smaller than \(90^\circ\) are acute angles.

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

Question 5. A _______ angle is larger than a straight angle.
(a) reflex
(b) right
(c) straight
(d) complete
Answer: (a) reflex
An angle that is greater than \(180^\circ\) (a straight angle) and less than \(360^\circ\) is called a reflex angle.
In simple words: An angle bigger than a straight line but smaller than a full circle is a reflex angle.

Exam Tip: Straight angle = \(180^\circ\); Reflex angle is between \(180^\circ\) and \(360^\circ\).

Question 6. How many degrees are there in half a revolution?
(a) \(180^\circ\)
(b) \(90^\circ\)
(c) \(270^\circ\)
(d) \(360^\circ\)
Answer: (a) \(180^\circ\)
A full revolution is \(360^\circ\). Therefore, half a revolution is \(\frac{1}{2} \times 360^\circ = 180^\circ\).
In simple words: Half of a full circle is \(180^\circ\).

Question 7. How many right angles make 180°?
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (c) 2
Each right angle is \(90^\circ\). To get \(180^\circ\), we need \(\frac{180^\circ}{90^\circ} = 2\) right angles.
In simple words: Two right angles equal \(180^\circ\).

Exam Tip: \(90^\circ + 90^\circ = 180^\circ\).

Question 8. How many right angles make 360°?
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (d) 4
A complete revolution is \(360^\circ\). Dividing by \(90^\circ\), we get \(\frac{360^\circ}{90^\circ} = 4\) right angles.
In simple words: Four right angles make a full circle.

Exam Tip: A full circle has four quadrants of \(90^\circ\) each.

Question 9. Which of the following is model for perpendicular lines?
(a) The parallel edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter ‘L’.
(d) The letter ‘V’.
Answer: (c) The line segments forming the letter ‘L’.
Perpendicular lines meet at a right angle (\(90^\circ\)), which is clearly visible in the standard font letter 'L'.
In simple words: The letter 'L' has standing and sleeping lines meeting at a right angle.

Exam Tip: Perpendicular lines always form a square corner (\(90^\circ\)).

Question 10. What is the angle name for one-fourth revolution?
(a) straight angle
(b) right angle
(c) complete angle
(d) none of these
Answer: (b) right angle
One-fourth of a full revolution equals \(\frac{1}{4} \times 360^\circ = 90^\circ\), which is a right angle.
In simple words: One-fourth of a circle is a right angle.

Exam Tip: One-fourth revolution = \(90^\circ\); Half revolution = \(180^\circ\); Full revolution = \(360^\circ\).

Question 11. Find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 6.
(a) 3
(b) 2
(c) 1
(d) 0
Answer: (c) 1
When the hour hand moves from 3 to 6, it covers 3 hour spaces, which is a quarter turn or \(90^\circ\) (1 right angle).
In simple words: Moving from 3 to 6 on a clock covers 90 degrees, which is 1 right angle.

Exam Tip: Each hour space on a clock face represents \(30^\circ\). Moving 3 hours = \(3 \times 30^\circ = 90^\circ\).

Question 12. If an angle is larger than a right angle, but less than a straight angle, it is called an _________.
(a) right angle
(b) straight angle
(c) acute angle
(d) obtuse angle
Answer: (d) obtuse angle
An angle measuring between \(90^\circ\) and \(180^\circ\) is an obtuse angle.
In simple words: An angle bigger than a right angle but smaller than a straight line is obtuse.

Exam Tip: Acute \(< 90^\circ\), Right \(= 90^\circ\), Obtuse between \(90^\circ\) and \(180^\circ\).

Question 13. There are __________ main directions.
(a) 4
(b) 3
(c) 2
(d) 1
Answer: (a) 4
The four main (cardinal) directions are North, South, East, and West.
In simple words: There are 4 main directions: North, South, East, and West.

Exam Tip: Each adjacent main direction forms a \(90^\circ\) angle with the next.

II. Fill in the blanks:

Question 14. A __________ is a polygon which has four sides.
Answer: quadrilateral
A polygon enclosed by four line segments is called a quadrilateral.
In simple words: A four-sided closed shape is a quadrilateral.

Exam Tip: Examples of quadrilaterals include rectangles, squares, and parallelograms.

Question 15. Each angle of a rectangle is a _________ angle.
Answer: right
A rectangle has four right angles, each measuring \(90^\circ\).
In simple words: The corners of a rectangle are all right angles (\(90^\circ\)).

Exam Tip: A rectangle and a square both have four right angles.

Question 16. Two faces meet at a line segment called an _______.
Answer: edge
In a 3D solid, the line segment where two flat faces meet is called an edge.
In simple words: The line where two faces join is an edge.

Exam Tip: Faces meet at edges, and edges meet at vertices (corners).

Question 17. The cylinder, the cone and the sphere have no __________ edges.
Answer: straight
Cylinders, cones, and spheres involve curved surfaces and curved circular rims, possessing no straight line segments as edges.
In simple words: These shapes have curved boundaries instead of straight edges.

Exam Tip: Spheres have 0 faces, 0 edges, and 0 vertices.

Question 18. When the sum of the measures of two angles is that of a right angle, then each one of them is _____________.
Answer: acute
If two angles add up to \(90^\circ\) (a right angle), both must individually be less than \(90^\circ\), making them acute angles.
In simple words: If two angles together make a right angle, each individual angle must be acute.

Exam Tip: Such pairs of angles are called complementary angles.

Question 19. When two lines intersect and the angle between them is a right angle, then the lines are said to be _______________.
Answer: perpendicular
Lines that intersect at an angle of \(90^\circ\) are perpendicular to each other.
In simple words: Intersecting lines at right angles are perpendicular.

Exam Tip: The symbol for perpendicular is \(\perp\).

Question 20. A line segment is a fixed portion of a _________.
Answer: line
A line extends endlessly in both directions; a line segment is a finite portion of that line with two distinct endpoints.
In simple words: A line segment is a piece cut out from a straight line.

Exam Tip: A line has no endpoints, a ray has 1 endpoint, and a line segment has 2 endpoints.

Question 21. The angle for one revolution is a __________________.
Answer: complete angle (or \(360^\circ\))
A full rotation around a point measures \(360^\circ\), which is termed a complete angle.
In simple words: A full circle turn is a complete angle of \(360^\circ\).

Exam Tip: Complete angle = \(360^\circ\).

III. Do as directed:

Question 22. Which direction will you face if you start facing:
(a) south and make one full revolution?
(b) east and make half of a revolution clockwise?
Answer:
(a) Facing South and making one full revolution (\(360^\circ\)) brings you back to facing South.
(b) Facing East and making half a revolution (\(180^\circ\)) clockwise brings you to facing West.
In simple words: (a) Full turn returns to the same direction (South). (b) Half turn opposite to East is West.

Exam Tip: A full turn brings you to your original direction; half turn points you in the exact opposite direction.

Question 23. How many right angles do you make if you start facing:
(a) south and turn clockwise to west?
(b) north and turn anti-clockwise to east?
Answer:
(a) From South to West clockwise is a \(90^\circ\) turn, which is 1 right angle.
(b) From North to East anti-clockwise passes through West, covering \(270^\circ\), which equals 3 right angles.
In simple words: (a) South to West clockwise is 1 right angle. (b) North to East anti-clockwise covers 3 right angles.

Exam Tip: Each step between adjacent main directions (North-East-South-West) represents 1 right angle (\(90^\circ\)).

Question 24. Describe the types of triangles on the basis of angles.
Answer:
Triangles are classified into three types based on their interior angles:
1. Acute-angled triangle: All three angles are acute (less than \(90^\circ\)).
2. Right-angled triangle: Exactly one angle is a right angle (\(90^\circ\)).
3. Obtuse-angled triangle: Exactly one angle is obtuse (greater than \(90^\circ\)).
In simple words: Triangles are named by angles as acute (all small), right (one \(90^\circ\)), or obtuse (one large).

Exam Tip: The sum of all three angles in any triangle is always \(180^\circ\).

Question 25. Find the angle measure between the hands of the clock in each figure:
(a) 9:00 a.m.
(b) 6:00 p.m.
Answer:
(a) At 9:00 a.m., the minute hand is at 12 and the hour hand is at 9. This spans 3 hour spaces (\(3 \times 30^\circ = 90^\circ\)), which is a right angle (\(90^\circ\)).
(b) At 6:00 p.m., the minute hand is at 12 and the hour hand is at 6. This spans 6 hour spaces (\(6 \times 30^\circ = 180^\circ\)), which is a straight angle (\(180^\circ\)).
In simple words: (a) 9 o'clock forms a \(90^\circ\) right angle. (b) 6 o'clock forms a \(180^\circ\) straight angle.

Exam Tip: Each hour mark on a clock dial represents \(30^\circ\) (\(360^\circ \div 12\)).

Question 26. How many angles are formed in the figures (i), (ii) and (iii)? Name them.
Answer:
(i) Triangle ABC has 3 angles: \(\angle ABC\), \(\angle BCA\), and \(\angle CAB\).
(ii) Quadrilateral ABDC has 4 angles: \(\angle ABD\), \(\angle BDA\), \(\angle DAC\), and \(\angle ACD\) (or considering the main vertices A, B, C, D: \(\angle DAB\), \(\angle ABC\), \(\angle BCD\), \(\angle CDA\)).
(iii) The composite figure with intersecting line segments forms multiple angles: \(\angle DAB\), \(\angle DAC\), \(\angle CAB\), \(\angle ABC\), \(\angle ACB\), and \(\angle ADC\).
In simple words: Count the corners where lines meet in each polygon. Figure (i) has 3 angles, figure (ii) has 4 angles, and figure (iii) has multiple angles formed by intersecting lines.

Exam Tip: The number of interior angles in a polygon equals the number of its vertices or sides.

Question 27. A ship sailing in river Jhelam moves towards east. If it changes to north, through what angle does it turn?
Answer:
From East to North is a quarter turn in the clockwise direction, which measures \(90^\circ\) (a right angle).
In simple words: Turning from East to North covers a \(90^\circ\) right angle.

Exam Tip: Adjacent cardinal directions (East to North, North to West, etc.) always form a \(90^\circ\) angle.

Question 28. A bicycle wheel makes four and a half turns. Find the number of right angles through which it turns.
Answer:
1 full turn = 4 right angles (\(360^\circ\))
4 full turns = \(4 \times 4 = 16\) right angles
Half turn = 2 right angles (\(180^\circ\))
Total right angles = \(16 + 2 = 18\)
In simple words: Each full turn has 4 right angles. For 4.5 turns, multiply \(4.5 \times 4 = 18\) right angles.

Question 29. Which of the following statements are true:
(i) The vertex of an angle lies in its interior.
(ii) The vertex of an angle lies in its exterior.
(iii) The vertex of an angle lies on it.
Answer:
Statement (iii) is true: The vertex of an angle always lies on the angle itself (it is the common endpoint where the two arms meet).
In simple words: The vertex is the corner point, so it lies directly on the angle.

Exam Tip: The vertex is never in the interior or exterior; it forms the corner point of the angle.

Question 30. In figure, which of the following statements are true:
(i) Point B is the interior of \(\angle AOB\).
(ii) Point B is the interior of \(\angle AOC\).
(iii) Point A is the interior of \(\angle AOD\).
(iv) Point C is the exterior of \(\angle AOB\).
(v) Point D is the exterior of \(\angle AOC\).
Answer:
Based on standard geometric ray configurations (where rays OA, OB, OC, OD emerge from vertex O in order):
- Point B lies on the ray OB, which forms the boundary of \(\angle AOB\), so (i) is false (it lies on the arm, not strictly in the interior).
- Point B lies between ray OA and ray OC, so point B is in the interior of \(\angle AOC\). Thus, (ii) is true.
- Point A lies on the ray OA (boundary), so (iii) is false.
- Point C lies outside the region between OA and OB, so Point C is in the exterior of \(\angle AOB\). Thus, (iv) is true.
- Point D lies outside the region between OA and OC, so Point D is in the exterior of \(\angle AOC\). Thus, (v) is true.
In simple words: Statements (ii), (iv), and (v) are true because they correctly identify points lying inside or outside the respective angle regions.

Exam Tip: Interior means strictly between the two arms of the angle; exterior means outside the arms.