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

erm.. that is not right...

Answer 2

To find the measure of \( \angle D \), we need to first establish the relationship between the angles based on their positions.

Given that the vertical line and the upward slanting line form angles \( A \) and \( D \), we note that \( \angle A \) and \( \angle D \) are adjacent angles formed by the intersecting lines. In many intersecting line scenarios, adjacent angles are supplementary, meaning that their measures sum to \( 180^\circ \).

Thus, we write the equation:

\[
m\angle A + m\angle D = 180^\circ
\]

Substituting the expressions for \( m\angle A \) and \( m\angle D \):

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

Combining like terms:

\[
4x + 2x - 10 + 22 = 180
\]
\[
6x + 12 = 180
\]

Next, we subtract \( 12 \) from both sides:

\[
6x = 168
\]

Now we divide by \( 6 \):

\[
x = 28
\]

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

\[
m\angle D = 2x + 22
\]
\[
m\angle D = 2(28) + 22
\]
\[
m\angle D = 56 + 22
\]
\[
m\angle D = 78
\]

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

\[
\boxed{78^\circ}
\]