Two supplementary angles have the following measures: m∠ABC=135°

Question

and m∠CBD=9x°
. What is the equation to solve for x
?(1 point)
Responses

9x°=180°
9 x equals 180

9x°−135°=180°
9 x minus 135 equals 180

9x°+135°=180°
9 x plus 135 equals 180

9x°+135°=90°

Answer 1

To determine the correct equation for the problem involving supplementary angles, we start by recalling that supplementary angles add up to 180°. Given:

• m∠ABC = 135°
• m∠CBD = 9x°

Since these angles are supplementary, we can set up the equation:

\[ m∠ABC + m∠CBD = 180° \]

Substituting the given values:

\[ 135° + 9x° = 180° \]

To solve for x, we can simplify this equation. Rearranging it gives:

\[ 9x° = 180° - 135° \] \[ 9x° = 45° \]

Thus, the equation to solve for x is:

\[ 9x° + 135° = 180° \]

So the correct response is:

9x° + 135° = 180°