Question

Given the figure below, find the values of x and z.
120°
(8x
+ 96).

Answer 1

x = 3; z = 60°

Explanation:

x:

The angles measuring 120° and (8x + 96)° are vertical angles, which means they're congruent and equal.

Thus, we can solve for x by setting the two angles equal to each other and isolate x:

`120=8x+96\\24=8x\\3=x`

We can check our answer by plugging in 3 for x and ensure that we get 120:

`120=8(3)+96\\120=24+96\\120=120`

z:

We see that a horizontal straight line separates the angle measuring 120° and z°. Straight lines create straight angles, which equal 180°.

Thus, we can find the measure of z by adding the 120° angle and the z° and set them equal to 180. Then, we must isolate z:

`120+z=180\\z=60`