Use facts about supplementary angles to solve the following problem. Two angles are supplementary and have measures m∠ABC=15°

Question

and m∠CBD=x°
. What is the value of m∠CBD
?(1 point)
Responses

180°
180 degrees

165°
165 degrees

75°
75 degrees

15°
15 degrees

Answer 1

Two angles are supplementary if the sum of their measures is 180 degrees. Given that \( m∠ABC = 15° \) and \( m∠CBD = x° \), we can set up the equation:

\[ m∠ABC + m∠CBD = 180° \]

Substituting the known value:

\[ 15° + x° = 180° \]

To find \( x \), we subtract 15° from both sides:

\[ x = 180° - 15° \]

Calculating this gives:

\[ x = 165° \]

Therefore, the value of \( m∠CBD \) is \( 165° \).

The answer is 165°.