﻿ Angles Word Problems | Problems & Solutions

# Angles Word Problems

Angles Word Problems
• Page 1
1.
Pick the two pairs of vertical angles.

 a. $\angle$2 and $\angle$4 b. $\angle$1, $\angle$3 and $\angle$2, $\angle$4 c. $\angle$1 and $\angle$3 d. $\angle$4, $\angle$3 and $\angle$2, $\angle$1

#### Solution:

When two lines intersect, two pairs of congruent opposite angles are formed. angles in each such pair are called vertical angles.

1, 3 and 2, 4 are two pairs of vertical angles.

2.
Find the measure of $\angle$$x$.

 a. 130 b. 60 c. 135 d. 120

#### Solution:

45° + x = 180°.
[Straight angle.]

x = 180° - 45° = 135°
[Subtract 45° from each side.]

The measure of x = 135.

3.
UO and UT are opposite rays. What is the measure of $\angle$RUN?

 a. 100o b. 125o c. 120o d. None of the above

#### Solution:

From the figure, OUT = 180o
[Since UO and UT are opposite rays.]

So, OUR + RUP + PUN + NUT = 180o.

32o + x + 43o + 23o = 180o
[Substitute OUR = 32o, PUN = 43o and Ð NUT = 23o.]

x + 98o =180o.

x = 180o - 98o = 82o
[Subtract 98o on both sides.]

RUN = x + PUN.

RUN = 82o + 43o = 125o
[Substitute x = 82o and PUN = 43o.]

4.
What are the measures of $\angle$$b$, $\angle$$c$ and $\angle$$d$, if $\angle$$a$ = 90o in the figure?

 a. 90o, 90o and 90o b. 90o, 30o and 60o c. 40o, 140o and 40o d. None of the above

#### Solution:

From the figure, 50o + d = 90o.
[50o and d are complementary angles.]

d = 90o - 50o = 40o
[Subtract 50o on both sides and simplify.]

d and c, c and b form linear pairs.

Sum of the angles forming linear pairs is 180o.

d + c = 180o.

40o + c = 180o
[Substitute d = 40o.]

c = 180o - 40o = 140o
[Subtract 40o on both sides and simplify.]

c + b =180o.

140o + b = 180o
[Substitute c = 140o.]

b = 180o - 140o = 40o
[Subtract 140o on both sides and simplify.]

5.
What are the exterior angles in the figure?

 a. Ã1, Ã2, Ã11 and Ã12 b. Ã1, Ã2, Ã8 and Ã7 c. Ã11, Ã12, Ã3 and Ã4 d. Ã2, Ã4, Ã11 and Ã9

#### Solution:

When a transversal intersects a set of parallel lines, the angles formed outside the parallel lines are called exterior angles.

From the figure, 1, 2, 11 and 12 are the angles formed outside the parallel lines P, Q and R.

Exterior angles in the figure are 1, 2, 11 and 12.

6.
Find $m$$\angle$COD.

 a. 90° b. 180° c. 60° d. 120°

7.
Find $m$$\angle$AOC.

 a. 180° b. 120° c. 90° d. 60°

8.

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

9.
Identify a pair of angles that are vertical to each other.

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

What is $\angle$BOA, if $\angle$COA = 78° and $\angle$COB = 27° in the figure?