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)
°
To find the measure of angle D, we can set up an equation by setting the measure of angle D equal to (2x+22)°:
m∠D = (2x+22)°
Since we know that m∠D = (2x+22)°, we can use the given information that m∠A = (4x-10)° to solve for x.
Since angles A and D are vertical angles, they are congruent. Therefore, we can set the measure of angle A equal to the measure of angle D:
m∠A = m∠D
(4x-10)° = (2x+22)°
Now we can solve for x:
4x - 10 = 2x + 22
2x = 32
x = 16
Now that we have found the value of x, we can substitute it back into the equation for angle D:
m∠D = 2(16) + 22
m∠D = 32 + 22
m∠D = 54°
Therefore, the measure of angle D is 54°.
If there are two supplementary angles, ∠D
and ∠E
, where m∠D=(4x+8)° and m∠E=(x+17)° , and ∠F is a vertical angle with ∠D , what is the measure of ∠F ?
(1 point)
Responses
124°
124 degrees
132°
132 degrees
31°
31 degrees
48°
To find the measure of angle F, we need to use the information given that angles D and E are supplementary (meaning they add up to 180 degrees) and that angle F is a vertical angle to angle D.
Given:
m∠D = (4x+8)°
m∠E = (x+17)°
Since angles D and E are supplementary, we can set up an equation:
m∠D + m∠E = 180
(4x+8) + (x+17) = 180
5x + 25 = 180
5x = 155
x = 31
Now that we have found the value of x, we can substitute it back into the equation for angle F. Since angle F is vertical to angle D, angle F has the same measure as angle D.
m∠F = m∠D
m∠F = 4(31) + 8
m∠F = 124 + 8
m∠F = 132°
Therefore, the measure of angle F is 132°.