Use facts about supplementary angles to solve the following problem. Two angles are supplementary and have measures m∠ABC=15° and m∠CBD=x°. What is the value of m∠CBD?
A 180
B 15
C 165
D 75
The sum of the measures of supplementary angles is always 180 degrees. In this problem, we are given that m∠ABC + m∠CBD = 180 degrees. Substituting in the given measure of m∠ABC (15 degrees), we have:
15 degrees + m∠CBD = 180 degrees
Simplifying the equation, we find:
m∠CBD = 180 degrees - 15 degrees
m∠CBD = 165 degrees
Therefore, the value of m∠CBD is 165 degrees. The answer is C.