Angles | Math Olympiad for Class 5 PDF Download

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Q1. When the clock shows 3:00, what type of angle is formed between the hour and minute hands?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (b) Right angle

At 3:00, the hour hand is on 3 and the minute hand is on 12. 
Each number on the clock is 30° apart (360° ÷ 12 = 30°). 
From 12 to 3 is 3 steps, so 3 × 30° = 90°. 
A 90° angle is a right angle.

Q2. A pizza is cut into 4 equal slices. What is the angle at the pointy end of each slice?
(a) 60°
(b) 90°
(c) 120°
(d) 180°
Ans: (b) 90°

 A full pizza is a circle, which is 360°.
 If it’s cut into 4 equal slices, each slice has an angle of 360° ÷ 4 = 90°. 
So, the angle at the pointy end of each slice is 90°.

Q3. When you open a book halfway, the angle between the covers is 180°. What type of angle is this?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (d) Straight angle

 A straight angle measures 180°, forming a straight line. 
When a book is opened halfway so the covers are flat, the angle between them is 180°, which is a straight angle.

Q4. At 6:00, what is the angle between the hour and minute hands of a clock?
(a) 90°
(b) 120°
(c) 180°
(d) 360°
Ans: (c) 180°

At 6:00, the hour hand is on 6 and the minute hand is on 12.
The distance between 12 and 6 is 6 steps, and each step is 30° (360° ÷ 12 = 30°). So, 6 × 30° = 180°. 
The angle is 180°, a straight angle.

Q5. A ladder leans against a wall, forming a 45° angle with the ground. What type of angle is this?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (a) Acute angle

An acute angle is less than 90°. Since 45° is less than 90°, the angle between the ladder and the ground is an acute angle.

Q6. A rectangular picture frame has four corners. What is the measure of each angle in the frame?
(a) 45°
(b) 90°
(c) 120°
(d) 180°
Ans: (b) 90°

A rectangle has four right angles, and the sum of its angles is 360°. 
Each angle = 360° ÷ 4 = 90°. 
So, each corner of the frame is 90°.

Q7. When the clock shows 4:00, what is the angle between the hour and minute hands?
(a) 60°
(b) 90°
(c) 120°
(d) 150°
Ans: (c) 120°

At 4:00, the hour hand is on 4 and the minute hand is on 12. 
The distance from 12 to 4 is 4 steps, and each step is 30° (360° ÷ 12 = 30°). So, 4 × 30° = 120°. 
The angle is 120°, an obtuse angle.

Q8. A kite’s frame has two sticks crossing at a 90° angle. What type of angle do the sticks form?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (b) Right angle

A right angle measures exactly 90°. If the sticks cross at 90°, they form a right angle.

Q9. A triangle is drawn on a sheet of paper, and one of its angles is 110°. What type of angle is this?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (c) Obtuse angle

An obtuse angle is greater than 90° but less than 180°. Since 110° is between 90° and 180°, it is an obtuse angle.

Q10. You fold a piece of paper to make a paper airplane, and the wing forms a 30° angle with the body. What type of angle is this?
(a) Acute angle
(b) Right angle
(c) Obtuse angle
(d) Straight angle
Ans: (a) Acute angle

An acute angle is less than 90°. Since 30° is less than 90°, the angle between the wing and the body is an acute angle.