Question
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Find Missing Angles Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
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Question
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)
°
Find Missing Angles Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
5 of 55 of 5 Items
Question
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)
°
Answers
GPT-4o mini
To find the measure of angle D, we first need to understand the relationships between the angles. Since angles A and D are vertical angles, they are equal. Therefore, we can set up the equation:
m∠A = m∠D
Given the values for the angles:
m∠A = (4x - 10)°
m∠D = (2x + 22)°
Setting these equal to each other, we have:
4x - 10 = 2x + 22
Now, let's solve for x:
1. Subtract 2x from both sides:
4x - 2x - 10 = 22
2x - 10 = 22
2. Add 10 to both sides:
2x = 32
3. Divide by 2:
x = 16
Now that we have the value for x, we can substitute it back into the expression for m∠D to find its measure:
m∠D = 2x + 22
m∠D = 2(16) + 22
m∠D = 32 + 22
m∠D = 54°
Therefore, the measure of angle D is 54°.
m∠A = m∠D
Given the values for the angles:
m∠A = (4x - 10)°
m∠D = (2x + 22)°
Setting these equal to each other, we have:
4x - 10 = 2x + 22
Now, let's solve for x:
1. Subtract 2x from both sides:
4x - 2x - 10 = 22
2x - 10 = 22
2. Add 10 to both sides:
2x = 32
3. Divide by 2:
x = 16
Now that we have the value for x, we can substitute it back into the expression for m∠D to find its measure:
m∠D = 2x + 22
m∠D = 2(16) + 22
m∠D = 32 + 22
m∠D = 54°
Therefore, the measure of angle D is 54°.