Question

In the diagram below, point U is on segment $\overline{BY}$ and the measure of angle BUG is 30 degrees greater than the measure of angle GUY:

Answer 1

Answer: 75

Step-by-step explanation:

We have angle BUG angle GUY = angle BUY = 180. If we let angle GUY = x, then

(x+30) + x = 180 Solving this equation gives x=75.

Answer 2

Using the definition of linear pair angles, the measure of angle GUY is: 75°.

What is a Linear Pair?

A linear pair are two angles on a straight line whose sum equals 180 degrees.

Thus:

m∠BUG = m∠GUY + 30°

Therefore:

m∠BUG + m∠GUY = 180°

Substitute

m∠GUY + 30 + m∠GUY = 180 (linear pair)

2(m∠GUY) + 30 = 180

2(m∠GUY) = 180 - 30

2(m∠GUY) = 150

m∠GUY = 150/2

m∠GUY = 75°

Therefore, using the definition of linear pair angles, the measure of angle GUY is: 75°.

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