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)
°
Remaining Attempts : 3

Answer 1

To find the measure of angle \( D \), we need to first identify the relationship between the angles \( A \) and \( D \). Given that \( m∠A = (4x - 10)° \) and \( m∠D = (2x + 22)° \), we look to see if they are related in a way that can help us set up an equation.

Since angles \( A \) and \( D \) are formed by intersecting lines, they are supplementary angles (their measures add up to 180 degrees). Therefore, we can write the equation:

\[ m∠A + m∠D = 180° \]

Substituting the expressions for angles \( A \) and \( D \):

\[ (4x - 10) + (2x + 22) = 180 \]

Now, we will combine like terms:

\[ 6x + 12 = 180 \]

Next, subtract 12 from both sides:

\[ 6x = 168 \]

Now, divide by 6:

\[ x = 28 \]

With the value of \( x \) found, we can now find \( m∠D \):

\[ m∠D = 2x + 22 \]

Substituting \( x = 28 \):

\[ m∠D = 2(28) + 22 = 56 + 22 = 78 \]

Therefore, the measure of \( ∠D \) is

\[ \boxed{78°} \]