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 value of ∠D ?
To find the value of ∠D, we need to set up an equation using the given information:
m∠A = (4x-10)°
m∠D = (2x+22)°
Since angles A and D are vertical angles, they are congruent. This means that their measurements are equal. So we can set up the equation:
(4x-10)° = (2x+22)°
To solve for x, we can start by subtracting 2x from both sides:
(4x-2x)-10 = (2x-2x)+22
Simplifying:
2x-10 = 22
Next, we can add 10 to both sides:
2x-10+10 = 22+10
Simplifying:
2x = 32
Finally, we can divide both sides by 2 to solve for x:
2x/2 = 32/2
Simplifying:
x = 16
Now that we have the value of x, we can substitute it back into the equation to find the value of ∠D:
m∠D = (2x+22)°
m∠D = (2*16+22)°
m∠D = (32+22)°
m∠D = 54°
So the value of ∠D is 54°.