Solve Equations with Supplementary Angles Quick Check

Question

3 of 53 of 5 Items
Question
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

165°
165 degrees

180°
180 degrees

75°
75 degrees

15°
15 degrees
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page 11 of 12

Answer 1

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

Given:

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

Since these angles are supplementary, we have:

\[ m∠ABC + m∠CBD = 180° \]

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

\[ 15° + x° = 180° \]

Now, to find \( x \):

\[ x = 180° - 15° \]

\[ x = 165° \]

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