Question

GEOMETRY HOMEWORK HELP! PLS!!

Answer 1

Answer:

x = 37°

Step-by-step explanation:

Given the triangle with two given exterior angles, m ∠107° and m ∠110°:

We can use the exterior angle theorem where it states that the measure of each exterior angle of a triangle is equal to the sum of the measures of the opposite and remote interior angles.

Start by finding the supplement of m ∠110°, that will serve as the other remote interior angle.

The supplement of ∠110° is:

∠110° + y  = 180°

Where y = represents the other unknown interior angle.

Subtract ∠110° from both sides:

∠110° - ∠110°  + y  = 180° - ∠110°

y =  70°

Therefore, the other remote interior angle is y = 70°. Now, we can determine the value of x by establishing the following equation:

107° = x° + 70°

Subtract 70 from both sides:

107° - 70° = x° + 70°- 70°

x = 37°