Question

Solve for
x =
m m m m

Answer 1

x = 17

Explanation:

The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of two remote interior angles

∠ KLM is an exterior angle opposite of ∠ JKL and ∠ KJL.

In this scenario, ∠ JKL and ∠ KJL are the two remote interior angles of ΔJKL, because they are opposite the exterior angle, but interior angles within the triangle.

Then, we can set up the following equation from the theorem:

9x-8 (exterior angle) = 7x-32 (remote interior angle 1) + 5x - 27 (remote interior angle 2)

9x - 8 = 7x - 32 + 5x - 27

9x - 8 = 12x - 59

Isolate X to one side:

3x = 51

x = 17