Use the image to answer the question.

Question

An illustration shows intersecting lines and rays. The resulting angles are labeled. A vertical line is intersected by an upward slanting line from left to right. A downward slanting ray extends from the point where the lines intersect to the bottom right. Starting from the top part of the vertical line, the first angle betwee the vertical line and the slanting line is labeled A. Moving clockwise, next angle is labeled Angle B, then Angle C, then Angle D, and then Angle E. All of the angles have degree signs next to their labels, but they do not have degree measurements.

In the diagram, m∠A=(4x−10)°
and m∠D=(2x+22)°
. What is the measure of ∠D
?

(1 point)

Answer 1

To find the measure of angle \( D \), we can use the fact that angles \( A \) and \( D \) are vertical angles and therefore equal in measure. The given equations for the angles are:

\[ m\angle A = (4x - 10)^\circ \] \[ m\angle D = (2x + 22)^\circ \]

Since \( m\angle A = m\angle D \), we have:

\[ 4x - 10 = 2x + 22 \]

Now, we can solve for \( x \):

1. Subtract \( 2x \) from both sides: \[ 4x - 2x - 10 = 22 \] \[ 2x - 10 = 22 \]

2. Next, add 10 to both sides: \[ 2x = 32 \]

3. Divide by 2: \[ x = 16 \]

Now that we have the value of \( x \), we can substitute it back into the equation for \( m\angle D \):

\[ m\angle D = 2x + 22 \] \[ m\angle D = 2(16) + 22 \] \[ m\angle D = 32 + 22 \] \[ m\angle D = 54 \]

Therefore, the measure of angle \( D \) is \( \boxed{54} \) degrees.