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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

Correct answer : (1)
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.

Correct answer : (3)
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.

Correct answer : (4)
4.
Which two angles are adjacent?

 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.

Correct answer : (3)
5.
Which two angles are adjacent?

 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.

Correct answer : (3)
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.

Correct answer : (4)
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.

Correct answer : (3)
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.

Correct answer : (2)
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.

Correct answer : (4)
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.

Correct answer : (2)

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