Addition and Subtraction of Angles

Q.

Find the angle which is complementary to itself. [1 MARK]

Q. If the supplement of an angle is 152°, then what is the complement of that angle?

1. ${62}^{\circ }$
2. ${38}^{\circ }$
3. ${28}^{\circ }$
4. ${52}^{\circ }$

Q.

Find the measure of the angle ACE.

1. $\angle ACE={105}^o$

2. $\angle ACE={115}^o$

3. $\angle ACE={150}^o$

4. $\angle ACE={95}^o$

Q.

In the given figure, AB = AC, D is a point on AC and E an AB such that AD = ED = EC = BC, The ratio \(\angle{BAC} : \angle{ABC} =\) ___

Q. Calculate the complementary angle of ${76}^{\circ }$

1. ${24}^{\circ }$
2. ${14}^{\circ }$
3. ${114}^{\circ }$
4. ${104}^{\circ }$

Q.

Sum of two adjacent angles is 180 degrees. if one angle is 35 degrees then, find the other.

1. 125 degrees

2. 155 degrees

3. 135 degrees

4. 145 degrees

Q.

Is it correct to say that the sum of an acute and an obtuse angle will always be equal to that of a reflex angle? Justify your answer with the help of an example.

Q.

Three rays originates from a point as shown. $\angle$AOB is ${60}^{\circ }$ and $\angle$AOC is ${15}^{\circ }$. Find $\angle$BOC.

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

2. ${45}^{\circ }$

3. ${75}^{\circ }$

4. ${30}^{\circ }$

Q.

An angle whose measure is the sum of measures of two right angles is ____________

Q.

State whether the given statement is true or false.

The sum of two acute angles is greater than a reflex angle.

1. True
2. False

Q. Sum of two adjacent angles is 90 degrees. If one angle is 15 degrees, then find the other.

1. 65 degrees
2. 15 degrees
3. 75 degrees
4. 35 degrees

Q.

Find the meassure of angle DCE.

1. $\angle DCE={30}^o$

2. $\angle DCE={115}^o$

3. $\angle DCE={55}^o$

4. $\angle DCE={75}^o$

Q. Two supplementary angles are in the ratio 3: 2. Find the measure of the smaller angle.

1. ${72}^o$
2. ${85}^o$
3. ${47}^o$
4. ${68}^o$

Q. Find the supplementary of ${30}^o$ angle.

Q.

If two complementary angles are in the ratio 3 :2, then find the measure of the greater angle.

1. ${55}^o$
2. ${54}^o$
3. ${36}^o$
4. ${42}^o$

Q.

There exist two supplementary angles such that one of them is ${30}^{\circ }$ and the other one is two times some arbitrary angle x. Find the value of x (in degrees).

1. 30

2. 150

3. 300

4. 75

Q.

Two supplementary angles are in the ratio 3: 2. Find the greater angle.

1. ${108}^o$

2. ${40}^{\circ }$

3. $0^{\circ }$

4. ${180}^{\circ }$

Q.

The sum of two angles is $180°$. If one angle is $100°$, then the other is ____.

Q. If $\angle A$ and $\angle B$ add up to 90°, then which of the following statements is true.

1. $\angle A$ is the supplement of $\angle B.$
2. $\angle B$ is the complement of $\angle A.$
3. $\angle B$ is the supplement of $\angle A.$
4. None of the above

Q. The sum of two consecutive angles is 90°. Find the angles.

1. ${44.5}^o$
2. ${45.5}^o$
3. ${46.5}^o$
4. ${47.5}^o$

Q.

Can we have two acute angles whose sum is a right angle? Why or why not?

Q.

Fill in the blanks with acute$,$ obtuse$,$ right or straight$:$

An angle whose measure is the sum of the measures of two right angle is ______

Q.

There exist two supplementary angles such that one of them is ${30}^{\circ }$ and the other one is two times some arbitrary angle x. Find the value of x (in degrees).

1. 150

2. 300

3. 75

4. 30

Q. Question 1
The angles between North and West and South and East are
(a) complementary
(b) supplementary
(c) both are acute
(d) both are obtuse

Q.

Angle ${30}^{\circ }$ and twice of another angle $x$ are supplementary angles. Find the value of $x$ (in degrees)___.

Q.

What is the measure of $\angle DAB$.

1. ${45}^{\circ }$

2. ${65}^{\circ }$

3. ${47}^{\circ }$

4. ${55}^{\circ }$

Q.

In the adjoining figure, when $AB=AC$ and $AP\perp BC$, then $AB>AP$.

1. AB = AP

2. AB < AP

Q.

Sunita knows that the sum of complementary angles is equal to ${90}^{\circ }$. She thinks that there can be a pair of complementary angles such that both of them are equal. Is she correct? If yes, then find such a pair of angle.

1. No, there exists no such pair of angles.

2. Yes, 45^o

3. Yes, 15^o

4. Yes, 30^o

Q. Two supplementary angles differ by ${48}^o$. Find the angles.

Q.

Consider the following figure:

A and B are points on the line $\overleftrightarrow{AB},\overleftrightarrow{OC},\overleftrightarrow{OD}and\overleftrightarrow{OE}$ are rays with point O on the line $\overleftrightarrow{AB}$ . The angles AOC, COD, DOB, AOE, EOB are given by a, b, c, x and y respectively.

Choose the incorrect statement:

1. x and y form a linear pair of angles

2. a + b + c = x + y

3. a + b + c + x + y = 360°

4. x and y are complementary