Question

The 2 lines that make an X have a A above the middle and between the 2 lines on the right side says (4x-5) Degrees and on the left side between the lines says (x+16) degrees. Use the properties of vertical angles to find the value of x.

Responses
A 55
B 33
C 77
D 99
Question 2
What is the measure of ∠A?
Responses
A 159°159°
B 163°163°
C 161°161°
D 157°

Answer 1

C 7

D 157°

Explanation:

You want to know the value of x and the measure of angle A in the given figure.

Vertical angles

The angles marked with x-expressions are vertical angles, so have the same measure.

(x +16)° = (4x -5)° . . . . . the angle measures are the same

21 = 3x . . . . . . . . . . . . divide by °, add 5-x to both sides

7 = x . . . . . . . . . . . . divide by 3

The value of x is 7.

Linear pair

The angles marked with x-expressions each form a linear pair with the angle marked A. That means they total 180°.

(x +16)° +A = 180°

A = 180° -23° = 157° . . . . . . . use x=7 and subtract 23

The measure of angle A is 157°.