Question

∠C and ​∠D​ are vertical angles with m∠C=−3x+58 and m∠D=x−2.



What is m∠D?



Enter your answer in the box.

Answer 1

Since angles \( \angle C \) and \( \angle D \) are vertical angles, they are equal, which means:

\[
m\angle C = m\angle D
\]

We have the expressions for the measurements of the angles:
- \( m\angle C = -3x + 58 \)
- \( m\angle D = x - 2 \)

Setting them equal to each other, we get:

\[
-3x + 58 = x - 2
\]

Now, we can solve for \( x \). First, add \( 3x \) to both sides:

\[
58 = 4x - 2
\]

Next, add \( 2 \) to both sides:

\[
60 = 4x
\]

Now, divide by \( 4 \):

\[
x = 15
\]

Now that we have the value of \( x \), we can find \( m\angle D \):

\[
m\angle D = x - 2 = 15 - 2 = 13
\]

Thus, the measurement of angle \( D \) is:

\[
\boxed{13}
\]