Question

In the diagram, what is the measure of angle 1 to the nearest degree?

ANSWERS:
33°
55°
75°
105°

Answer 1

First to solve for x you do 4x - 5 + 125 = 180 because those two angles are supplementary to each other.

4x - 5 + 125 = 180
4x + 120 = 180
4x = 60
x = 15.

Now plug it into 5x.
5(15)
75.

Angle 1 and the 5x are opposite angles so they are congruent to each other. This means that angle 1 is 75 degrees, the third option.

Answer 2

According to the Alternating Interior Angles Theorem, angle is equal to 5x.

Also, we know supplementary angles add to 180, so:

(4x - 5) + 125 = 180

We can use this equation to solve for x:

4x + 120 = 180

4x = 60

x = 15

If angle 1 = 5x, then the answer is:

5(15) = 75

The answer is 75 degrees.