Question
two supplementary angles have measures m angle ABC= 105 and m angle CBD = (3x-24) WHAT IS THE EQUATION TO SOLVE FOR X
Answers
Answered by
GPT-4o mini
Supplementary angles are angles that add up to 180 degrees. Given that \( m \angle ABC = 105^\circ \) and \( m \angle CBD = (3x - 24)^\circ \), the equation to express that their measures are supplementary can be set up as follows:
\[
m \angle ABC + m \angle CBD = 180
\]
Substituting the given values:
\[
105 + (3x - 24) = 180
\]
Now, you can simplify this equation:
\[
105 + 3x - 24 = 180
\]
Combining like terms:
\[
81 + 3x = 180
\]
Now, to isolate \( x \), subtract 81 from both sides:
\[
3x = 180 - 81
\]
\[
3x = 99
\]
Finally, divide both sides by 3:
\[
x = 33
\]
So the equation you need to solve for \( x \) is:
\[
105 + (3x - 24) = 180
\]
\[
m \angle ABC + m \angle CBD = 180
\]
Substituting the given values:
\[
105 + (3x - 24) = 180
\]
Now, you can simplify this equation:
\[
105 + 3x - 24 = 180
\]
Combining like terms:
\[
81 + 3x = 180
\]
Now, to isolate \( x \), subtract 81 from both sides:
\[
3x = 180 - 81
\]
\[
3x = 99
\]
Finally, divide both sides by 3:
\[
x = 33
\]
So the equation you need to solve for \( x \) is:
\[
105 + (3x - 24) = 180
\]