Question

The measure of angle 1 is (3x+10) and the measure of angle 4 is (4x-15). What is the measure of angle 7?

Answer 1

95°

Explanation:

Vertical angles are congruent, so angles 1 and 4 will be congruent

Set up the angle measures equal to each other and solve for x:

3x + 10 = 4x - 15

10 = x - 15

25 = x

Angle 7 will be supplementary to angle 4, so we can set up another equation:

First, find the measure of angle 4 by plugging in 25 as x:

4x - 15

4(25) - 15

= 85

Then, find angle 7 by subtracting the measure of angle 4 from 180:

180 - 85

= 95

So, the measure of angle 7 is 95°