Find the value of x. Part 2c

Work Shown:

Let's label angle 2 as y, so y = x+132.

Also, let's add another variable z. We'll make z equal to the angle adjacent and supplementary to angle y. So y+z = 180

Solve for z to get

z = 180-y

z = 180-(x+132)

z = 180-x-132

z = 48-x

This angle z is added to the 90 degree angle to get the measure of the exterior angle 150 degrees. This is through the remote interior angle theorem.

So,

z+90 = 150

48-x+90 = 150

138-x = 150

-x = 150-138

-x = 12

x = -12

x = -12

Step-by-step explanation:

a) right triangle, bottom right angle: Using the Linear Pair postulate, 180° - 150° = 30°

b) right triangle, top angle: congruent sides implies congruent angles = 30°

c) left triangle, top angle: Using Complimentary Angles, 90° - 30° = 60°

d) left triangle, bottom left angle: congruent sides implies congruent angles = 60°

Using the Linear Pair Postulate:

∠2 + 60° = 180°

∠2           = 120°

x + 132   = 120

       x    = -12

the first option is the answer.