Question
Angle Pairs Unit Test
9 of 159 of 15 Items
Question
Two supplementary angles have measures m∠ABC=105°
and m∠CBD=(3x−24)°
. What is the equation to solve for x
? (1 point)
(3x−24)°+
°=
°
Answers
GPT-4o mini
To find the equation to solve for \( x \) given that angles \( \angle ABC \) and \( \angle CBD \) are supplementary, we start with the definition of supplementary angles. Two angles are supplementary if the sum of their measures is \( 180^\circ \).
Given:
- \( m\angle ABC = 105^\circ \)
- \( m\angle CBD = (3x - 24)^\circ \)
Since they are supplementary, we can write the equation as:
\[
m\angle ABC + m\angle CBD = 180^\circ
\]
Substituting in the values we have:
\[
105^\circ + (3x - 24)^\circ = 180^\circ
\]
Thus, the equation to solve for \( x \) is:
\[
105 + (3x - 24) = 180
\]
You can simplify and solve this equation to find the value of \( x \).
Given:
- \( m\angle ABC = 105^\circ \)
- \( m\angle CBD = (3x - 24)^\circ \)
Since they are supplementary, we can write the equation as:
\[
m\angle ABC + m\angle CBD = 180^\circ
\]
Substituting in the values we have:
\[
105^\circ + (3x - 24)^\circ = 180^\circ
\]
Thus, the equation to solve for \( x \) is:
\[
105 + (3x - 24) = 180
\]
You can simplify and solve this equation to find the value of \( x \).