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

75°
75 degrees

165°
165 degrees

180°
180 degrees

15°

1 answer

Supplementary angles are two angles whose measures add up to 180 degrees. Given that:

  • \( m∠ABC = 15° \)
  • \( m∠CBD = x° \)

We can set up the equation:

\[ m∠ABC + m∠CBD = 180° \]

Substituting the value of \( m∠ABC \):

\[ 15° + x° = 180° \]

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

\[ x° = 180° - 15° \]

\[ x° = 165° \]

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

The correct response is:

165°