Hello!

We are given that the measure of one angle is equal to 115 degrees (for convenience, we’ll refer to this angle as ∠W). Looking at the image above, we can see that ∠W and ∠Y are supplementary angles. Supplementary angles are two angles whose measures add to a sum of 180 degrees, also known as a straight line. This relationship can be expressed using the following formula:

A1 + A2 = 180

Now insert any known values provided by the image above:

(115) + (∠Y) = 180

Subtract 115 from both sides of the equation:

∠Y = 65

We have now proven that ∠Y has a measure of 65 degrees. Now, looking at the image again, we can see that ∠W and ∠X are vertical angles. Vertical angles are two angles that lie on opposite sides of two intersecting lines. A pair of vertical angles is always equal in measure. This relationship can be expressed using the following formula:

A1 = A2

Now insert any known values provided by the image above:

(∠X) = (115)

We have now proven that ∠X has a measure of 115 degrees.

I hope this helps!

7 0

3 years ago