Angles about a Point

Q.

Find the angle between the hour hand and minute hand when the clock shows 2 p.m.

Q.

A protractor has a semi-circular shape.

1. Triangle

2. Circle

Q.

Find the value of x in the following figure.

1. ${60}^{\circ }$

2. ${110}^{\circ }$

3. ${70}^{\circ }$

4. ${130}^{\circ }$

Q. The area of a square formed by combining two squares of side 3 cm is

1. 6 sq cm
2. 9 sq cm
3. 18 sq cm
4. 24 sq cm

Q.

A circular cake is to be equally distributed among 12 friends. If the cake has to be cut along its radius, what is the angle between consecutive cuts?

1. ${12}^{\circ }$

2. ${30}^{\circ }$

3. ${36}^{\circ }$

4. ${15}^{\circ }$

Q. Find the value of angle DAE in degrees.

1. 130
2. 90
3. 50
4. 40

Q.

Some rays are originating from a point. Sum of all the angles formed between the rays is independent of the number of rays.

1. False

2. True

Q. How many square feet in a square yard?

Q. Calculate the area of the shaded region in each of the figures given below:

Q.

In an analog watch, the minute hand is at 12. The angle between the hour hand and the minute hand is ${150}^{\circ }$. What could be the time?

1. 7 o'clock only.

2. either 5 o'clock or 7 o'clock

3. 5 o'clock only.

4. either 4 o'clock or 8 o'clock.

Q. Find the value of angle CAE in degrees, if angles CAE and DAB are equal.

1. 130
2. 65
3. 50
4. 45

Q.

Reflex angle of 90^o is:

1. 270^o

2. 180^o

3. 310^o

4. 300^o

Q. The area of the green square in the given figure is _______ sq. m.

1. 30
2. 20
3. 50
4. 100

Q.

From a circular pizza, Rohan takes out a quarter of it by making two cuts along its radius. And then Krishna took half of the remaining by making a cut along the radius. What is the angle subtended at the centre by the leftover pizza?

1. ${135}^{\circ }$

2. ${90}^{\circ }$

3. ${145}^{\circ }$

4. ${120}^{\circ }$

Q.

A boy is moving towards north. He turns to his left by ${270}^{\circ }$. In which direction is he moving now?

1. East

2. North

3. West

4. South

Q. The area of a square is 200 cm². The length of its diagonal is

(a) 10 cm
(b) 20 cm
(c) $10\sqrt{2}$ cm
(d) 14.1 cm

Q.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

1. ${60}^{\circ }$

2. ${120}^{\circ }$

3. ${90}^{\circ }$

4. $0^{\circ }$

Q.

A boy goes around a circular park. What is the total angle subtended by him at the centre of the park when he completes 3 quarters of the circle?

1. ${270}^{\circ }$

2. ${90}^{\circ }$

3. ${135}^{\circ }$

4. ${240}^{\circ }$

Q. Mark (✓) against the correct answer
Each diagonal of a square is 14 cm long. Its area is

(a) 196 cm²
(b) 88 cm²
(c) 98 cm²
(d) 147 cm²

Q.

At the intersection of two lines, one of the angles can be more than ${180}^{\circ }$.

1. True

2. False

Q.

To mark $\left(\frac{1}{6}\right)th$ of a circle, what angle should be drawn at the center of the circle ?

1. ${90}^{\circ }$

2. ${80}^{\circ }$

3. ${45}^{\circ }$

4. ${60}^{\circ }$

Q.

A ray is drawn at an angle of '4x' to a line. From the same point another ray is drawn on the other side of the line at an angle of '5x', as shown. If the sum of the other two angles is ${225}^{\circ }$. Find the value of x.

1. ${15}^{\circ }$

2. ${30}^{\circ }$

3. ${60}^{\circ }$

4. ${10}^{\circ }$

Q.

The length of each side of a square land shown in the figure is (a + b) units. In the corner of this land there is a square portion of length ‘b’ units is useless. Find the area of the portion of the land which is useful.

Q.

Find the sum of angles about a point in degrees.

1. 250

2. 180

3. 360

4. 320

Q.

A ray is drawn at an angle of '4x' to a line. From the same point another ray is drawn on the other side of the line at an angle of '5x', as shown. If the sum of the other two angles is ${225}^{\circ }$. Find the value of x.

1. ${30}^{\circ }$

2. ${60}^{\circ }$

3. ${10}^{\circ }$

4. ${15}^{\circ }$

Q.

In an analog watch, the minute hand is at 12. The angle between the hour hand and the minute hand is ${150}^{\circ }$. What could be the time?

1. 5 o'clock only.

2. 7 o'clock only.

3. either 5 o'clock or 7 o'clock

4. either 4 o'clock or 8 o'clock.

Q. Calculate the area of the square ABED.

1. 64 sq. m
2. 50 sq. m
3. 32 sq. m
4. 16 sq. m

Q.

A boy is walking with a constant speed around a circular park. Initially the angle between the line joining his position to the centre and one of the radius of the park is ${30}^{\circ }$. After two minutes the angle between the line joining his position to the centre and the the same radius of the park is once again ${30}^{\circ }$. Find the total time that the boy takes to complete one round.

1. 12 minutes.

2. 24 minutes

3. 8 minutes

4. 6 minutes

Q.

At the intersection of two lines, one pair of opposite angles measures 90 degrees each. Find the angles of the other pair.

1. 90 degrees each

2. 145 degrees each

3. 180 degrees each

4. 45 degrees each

Q.

In the figure below, OP, OQ, OR and OS are four rays. Then, find $\frac{(\angle POQ+\angle QOR+\angle SOR+\angle POS)}{3}$.

1. ${60}^{\circ }$

2. $0^{\circ }$

3. ${90}^{\circ }$

4. ${120}^{\circ }$