CBSE Class 5 Mathematics Shapes And Angles Worksheet Set 01

Chapter-2: Shapes and Angles

Q1. Fill in the blanks:

Question 1(a). A right angle measures _____________________.
Answer: \(90^\circ\)
In simple words: A right angle is always exactly \(90^\circ\), just like the corner of a square.

Exam Tip: Memorize standard angle measurements: acute (\(< 90^\circ\)), right (\(= 90^\circ\)), obtuse (\(> 90^\circ\) and \(< 180^\circ\)), and straight (\(= 180^\circ\)).

Question 1(b). An ________________ angle is less than \(90^\circ\).
Answer: acute
In simple words: An angle measuring less than \(90^\circ\) is called an acute angle.

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

Question 1(c). A _________________ angle measures equal to two right angles.
Answer: straight
In simple words: Two right angles make \(90^\circ + 90^\circ = 180^\circ\), which is a straight angle.

Question 1(d). A straight angle always measures________________.
Answer: \(180^\circ\)
In simple words: A straight line represents an angle of \(180^\circ\).

Exam Tip: Always include the degree symbol (\(^\circ\)) when writing angle measurements.

Question 1(e). When I stretch all the five fingers of my hand to full, my fingers make four ________angles.
Answer: acute
In simple words: The space between any two adjacent stretched fingers forms an acute angle because it is less than \(90^\circ\).

Exam Tip: Visualize your hand spread out to understand the gaps between fingers.

Question 1(f). If I stand erect, barefeet , my foot makes a __________ angle with my leg.
Answer: right (or \(90^\circ\))
In simple words: Standing straight upright creates a perpendicular upright posture, forming a right angle between your foot and leg.

Exam Tip: Perpendicular lines always intersect at \(90^\circ\).

Question 1(g). Two rays with a common end point form an_________.
Answer: angle
In simple words: An angle is created when two rays share a common starting point called the vertex.

Exam Tip: Learn the precise geometric definition of an angle.

Question 1(h). The common end point is called the _______________.
Answer: vertex
In simple words: The corner point where two rays meet is known as the vertex.

Exam Tip: Vertex is a key geometric term used in naming angles.

Question 1(i). \(\frac{1}{2}\) of a straight angle is __________________.
Answer: \(90^\circ\) (or a right angle)
In simple words: Half of \(180^\circ\) is \(90^\circ\), which is a right angle.

Exam Tip: Fraction calculations with angles are very common in exams; remember that a straight angle is \(180^\circ\).

Question 1(j). There are ___________ \(30^\circ\) in a right angle.
Answer: 3
In simple words: Divide \(90^\circ\) by \(30^\circ\) to get 3 (\(90 \div 30 = 3\)).

Exam Tip: Division helps find how many smaller angles fit into a larger angle.

Q2. Make a closed shapes with:

Question 2(a). 4 sides
Answer: Quadrilateral (Example: Square or Rectangle)
In simple words: A closed shape with 4 straight sides is called a quadrilateral.

Exam Tip: Sketch a neat quadrilateral using a ruler and label its four vertices.

Question 2(b). 6 sides
Answer: Hexagon
In simple words: A closed shape with 6 straight sides is called a hexagon.

Exam Tip: Hex means six; remember the prefix for polygon names.

Question 2(c). 8 sides and also name them
Answer: Octagon
In simple words: A closed shape with 8 straight sides is called an octagon, similar to a stop sign.

Question 3. [Activity: Name written using straight line letters like A, H, M, N, Z]
Answer: Let us take the letter 'H' as an example:
a) Acute angles = 0
b) Obtuse angles = 0
c) Right angles = 4
d) Straight angles = 2 (formed by the horizontal crossbar and vertical stems)
In simple words: Depending on the letters of your name, count the corners carefully based on whether they measure less than, equal to, or greater than \(90^\circ\).

Exam Tip: Use block capital letters made entirely of straight segments for easy angle counting.

Question 4. Which shape is considered to be the most rigid shape? Give three examples where this shape is used?
Answer: Triangle.
Three examples where triangles are used for rigidity:
1. Roof trusses in houses and buildings.
2. Bridges and crane towers.
3. Electricity transmission pylons.
In simple words: A triangle is the most rigid shape because its sides cannot be changed without bending or breaking them, making structures very strong.

Exam Tip: Triangles provide structural stability because fixing the lengths of its three sides uniquely determines its shape.

Q5. Write what kind of angle is made by the hands of a clock at these times:

Question 5(a). 7:25
Answer: Obtuse angle
In simple words: At 7:25, the hour hand is near 7 and the minute hand is at 5, forming an angle greater than \(90^\circ\).

Exam Tip: Each minute space on a clock face represents \(6^\circ\) (\(360^\circ \div 60\)).

Question 5(b). 3 O’clock
Answer: Right angle (\(90^\circ\))
In simple words: At 3:00, the minute hand points at 12 and the hour hand points at 3, making an exact right angle.

Exam Tip: 3 o'clock, 9 o'clock, and 15-minute intervals form right angles.

Question 5(c). 6 O’clock
Answer: Straight angle (\(180^\circ\))
In simple words: At 6:00, the hands point in exact opposite directions, forming a straight line.

Question 5(d). 10:15
Answer: Obtuse angle
In simple words: At 10:15, the angle between the hour hand and minute hand is greater than \(90^\circ\).

Exam Tip: Always visualize or sketch the clock hands to verify angle types.

Q6. How many degrees is the angle which is:

Question 6(a). \(\frac{1}{2}\) of a right angle
Answer:
A right angle = \(90^\circ\)
\(\frac{1}{2} \times 90^\circ = 45^\circ\)
In simple words: Half of \(90^\circ\) is \(45^\circ\).

Exam Tip: Multiply the fraction directly by \(90^\circ\) for right angle problems.

Question 6(b). \(\frac{1}{3}\) of a right angle
Answer:
A right angle = \(90^\circ\)
\(\frac{1}{3} \times 90^\circ = 30^\circ\)
In simple words: One-third of \(90^\circ\) is \(30^\circ\).

Exam Tip: Divide \(90\) by \(3s\) to get \(30\).

Question 6(c). 2 times of right angle
Answer:
A right angle = \(90^\circ\)
\(2 \times 90^\circ = 180^\circ\)
In simple words: Twice a right angle is \(180^\circ\), which is a straight angle.

Exam Tip: Two right angles equal a straight angle.

Q7. Calculate the degree of the missing angles.

Question 7(a). Given \(\angle AOC = 90^\circ\) and \(\angle AOB = 35^\circ\), find \(\angle BOC\).
Answer:
\(\angle BOC = \angle AOC - \angle AOB\)
\(\angle BOC = 90^\circ - 35^\circ = 55^\circ\)
In simple words: Subtract the given inner angle from the total right angle to find the missing part.

Exam Tip: Adjacent angles that add up to a right angle are complementary.

Question 7(b). Given a straight line with an angle of \(75^\circ\) adjacent to the missing angle \(\angle HOI\). Find \(\angle HOI\).
Answer:
\(\angle HOI = 180^\circ - 75^\circ = 105^\circ\)
In simple words: Angles on a straight line add up to \(180^\circ\), so subtract \(75^\circ\) from \(180^\circ\).

Exam Tip: Linear pairs always sum to \(180^\circ\).

Question 7(c). Given \(\angle ADC = 125^\circ\), find the missing angle as indicated in the diagram.
Answer:
From the diagram, the total angle shown with the right-angle square marker and the outer extension corresponds to supplementary or complementary relationships. Assuming the standard problem where total angle is \(180^\circ\) or complementary to \(90^\circ\):
\(\angle ADB = 180^\circ - 125^\circ = 55^\circ\) (if forming a linear pair)
In simple words: Use angle sum properties of straight lines or right angles as shown in the specific diagram figure.

Exam Tip: Always check whether angles form a straight line (\(180^\circ\)) or a right angle (\(90^\circ\)).

Q8. Using a protractor draw the following angles: a) \(25^\circ\) b) \(90^\circ\) c) \(120^\circ\) d) \(45^\circ\)

Question 8. [Drawing Construction Steps]
Answer:
1. Draw a baseline ray with a starting endpoint.
2. Place the center of the protractor on the endpoint and the baseline along the \(0^\circ\) line.
3. Mark the required degree point (\(25^\circ\), \(90^\circ\), \(120^\circ\), or \(45^\circ\)) on the paper.
4. Join the endpoint to the marked point with a straight line.
In simple words: Use a protractor and ruler carefully to measure and draw each exact angle.

Exam Tip: Ensure the baseline of your protractor coincides exactly with the ray.

Question 9. Draw three different polygons having all angles equal.
Answer:
1. Equilateral Triangle (All 3 interior angles are \(60^\circ\))
2. Square / Regular Quadrilateral (All 4 interior angles are \(90^\circ\))
3. Regular Pentagon (All 5 interior angles are \(108^\circ\))
In simple words: Regular polygons have equal sides and equal interior angles. Examples include equilateral triangles, squares, and regular pentagons.

Exam Tip: Polygons with all equal angles and equal sides are called regular polygons.

Question 10. Name all the angles formed in the given figure and also classify them as acute, obtuse, right, straight angles.
Answer:
Referring to the multi-vertex polygon figure (A, B, C, D, E, F, G, H):
- Interior angles at vertices A, B, C, D, E, F, G, H are classified based on their openings.
- Corners with square symbols (like at E and F) are Right angles (\(90^\circ\)).
- Corners opening less than \(90^\circ\) are Acute angles.
- Corners opening wider than \(90^\circ\) are Obtuse angles.
In simple words: Inspect each corner of the polygon figure and measure or classify them using a protractor or visual comparison to a \(90^\circ\) corner.

Exam Tip: Look for the square symbol indicating right angles before classifying other corners.