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 ?(1 point)

Responses

180°
  180 degrees

15°
  15 degrees

165°
165 degrees

75°

1 answer

Two angles are supplementary if the sum of their measures is 180 degrees. In this case, we have:

\( m∠ABC = 15° \) \( m∠CBD = x° \)

Since these angles are supplementary, 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:

\[ x° = 180° - 15° \] \[ x° = 165° \]

Therefore, \( m∠CBD = 165° \).

The correct response is: 165 degrees.