Question
Two supplementary angles have the following measures: \( m \angle A B C=135^{\circ} \) and \( m \angle C B D=9 x \) What is the equation to solve for \( x \) ? (1 point)
Ask by Estrada Chen. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The equation to solve for \( x \) is:
\[
135 + 9x = 180
\]
Solution
To solve for \( x \), since the angles are supplementary, their measures add up to \( 180^\circ \).
Given:
\[
m \angle ABC = 135^\circ
\]
\[
m \angle CBD = 9x
\]
Set up the equation:
\[
135 + 9x = 180
\]
**Equation:**
\[
135 + 9x = 180
\]
Reviewed and approved by the UpStudy tutoring team
Like
error msg
Explain 
Simplify this solution Beyond the Answer
To find the value of \( x \), you first need to remember that supplementary angles add up to \( 180^{\circ} \). In this case, you can set up the equation: \[ 135^{\circ} + 9x = 180^{\circ} \] This equation represents the relationship between the two angles. Now you can solve for \( x \) by isolating it on one side! Subtract \( 135^{\circ} \) from both sides: \[ 9x = 180^{\circ} - 135^{\circ} \] Which simplifies to \( 9x = 45^{\circ} \). Now, divide both sides by 9 to find \( x \): \[ x = \frac{45^{\circ}}{9} = 5^{\circ} \]
