﻿ Properties of Special Angles Worksheet | Problems & Solutions

# Properties of Special Angles Worksheet

Properties of Special Angles Worksheet
• Page 1
1.
$\angle$A and $\angle$B are vertical angles. If m$\angle$A = 33o, then what is m$\angle$B?
 a. 33o b. 78o c. 147o d. None of the above

#### Solution:

mA = mB
[Measures of vertical angles are equal.]

mA = 33o

So, mB = 33o

2.
Lines AB and CD intersect at point O. Which of the following statements is/are always correct?

1. $\angle$AOC $\cong$ $\angle$DOB

2. m$\angle$COB = m$\angle$AOD

3. m$\angle$AOD + m$\angle$AOC = 180o

 a. 1 only b. 2 and 3 only c. 1, 2 and 3 d. 2 only

#### Solution:

AOC and DOB are congruent.
[Vertically opposite angles are congruent.]

mCOB = mAOD
[Vertically opposite angles are congruent.]

The angles AOD and AOC are linear pair of angles.

So, sum of their measures is 180o.

So, all the three statements are correct.

3.
Identify the figure in which the pairs of angles are not supplementary.

 a. Figure 1 only b. Figure 2 only c. Figure 3 only d. Figure 1 and Figure 2

#### Solution:

Two angles are said to be supplementary, if the sum of their measures is 180°.

In figures 1 and 2, the sum of the measures of the angles is not equal to 180°.

So, they are not supplementary angles.

4.

 a. $\angle$AOE and $\angle$BOC b. $\angle$AOB and $\angle$COD c. $\angle$AOB and $\angle$BOC d. $\angle$AOB and $\angle$EOD

#### Solution:

The angles sharing a common side are called as adjacent angles.

In the figure, AOB and BOC, BOC and COD, COD and DOE, DOE and EOA, and EOA and AOB are the angles sharing a common side.

So, among the choices AOB and BOC are the adjacent angles in the figure.

5.

 a. $\angle$AOC and $\angle$BOD b. $\angle$AOB and $\angle$BOA c. $\angle$AOB and $\angle$BOD d. $\angle$AOB and $\angle$COD

#### Solution:

The angles sharing a common side are called as adjacent angles.

In the figure, AOB and BOD, BOD and DOC, DOC and COA, and COA and AOB are the angles sharing a common side.

So, among the choices AOB and BOD are the adjacent angles in the figure.

6.
Identify the pair of angles that are vertical to each other.

 a. $\angle$AOB and $\angle$DOC b. $\angle$AOC and $\angle$COB c. $\angle$AOD and $\angle$AOC d. $\angle$AOC and $\angle$DOB

#### Solution:

Angles that are opposite to one another at the intersection of two lines are called vertical angles.

AOD and COB are the vertical pair.

7.
Choose the pair of angles that are adjacent to each other.

 a. $\angle$SWV and $\angle$VWS b. $\angle$SWV and $\angle$UWT c. $\angle$SWV and $\angle$VWU d. $\angle$VWU and $\angle$SWT

#### Solution:

The angles sharing a common side are called as adjacent angles.

In the figure, SWV and VWU, VWU and UWT, UWT and TWS, and TWS and SWV are the angles sharing a common side.

So, among the choices SWV and VWU are the adjacent angles in the figure.

8.
Choose the pair of angles that are supplementary to each other.

 a. $\angle$AOD and $\angle$COB b. $\angle$AOD and $\angle$DOB c. $\angle$AOC and $\angle$DOB d. $\angle$AOD and $\angle$DOA

#### Solution:

Two angles are called supplementary angles if the sum of their degree measurements is equal to 180°.

Among the choices, AOD and DOB are the supplementary angles.

9.
Identify the pair of angles that are adjacent to each other.

 a. $\angle$MQN and $\angle$MQO b. $\angle$MQN and $\angle$OQP c. $\angle$MQN and $\angle$MQP d. $\angle$MQN and $\angle$NQO

#### Solution:

The angles sharing a common side are called as adjacent angles.

In the figure, MQN and NQO, NQO and OQP are the angles sharing a common side.

So, among the choices MQN and NQO are the adjacent angles in the figure.

10.
Choose the pair of angles that are supplementary to each other.

 a. $\angle$AOC and $\angle$COA b. $\angle$AOC and $\angle$COD c. $\angle$AOC and $\angle$COB d. $\angle$AOB and $\angle$COD

#### Solution:

Two angles are called supplementary angles if the sum of their degree measurements is equal to 180°.

Among the choices, AOC and COD are the supplementary angles.