Use the image to answer the 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)
°
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Since angle A and angle D are alternate interior angles, they are congruent. Therefore, we can set up an equation:
m∠A = m∠D
4x-10 = 2x+22
First, let's isolate the x term by subtracting 2x from both sides:
4x - 2x - 10 = 2x - 2x + 22
2x - 10 = 22
Next, let's isolate the constant term by adding 10 to both sides:
2x - 10 + 10 = 22 + 10
2x = 32
Finally, let's solve for x by dividing both sides by 2:
2x/2 = 32/2
x = 16
Now we can substitute the value of x back into the equation for angle D:
m∠D = 2x + 22
m∠D = 2(16) + 22
m∠D = 32 + 22
m∠D = 54
Therefore, the measure of angle D is 54°.