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## Angle U and angle W are vertical angles. If the measure of angle U = 6x + 11 and the measure of angle W = 10x – 9, find the measure of

Question

Angle U and angle W are vertical angles. If the measure of angle U =

6x + 11 and the measure of angle W = 10x – 9, find the measure of angle U.

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Mathematics
3 years
2021-08-19T09:00:57+00:00
2021-08-19T09:00:57+00:00 2 Answers
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## Answers ( )

Answer:The measure of angle U is -9.46

Step-by-step explanation:You do not need the information about angle W to measure the angle of U. (So you can ignore all info about W).

U = 6x +11

By definition the incline of this line is 6.

tan(U) = 6/1

so angle U = arctan(6) = 80.54

It was given that U is an vertical angle. Since the difference between horizontal and vertical is 90 degrees, you can add 90 degrees.In this case you have an incline of -1/6

tan(U) = -1/6

so angle U = arctan(-1/6) = -9.46

The measure of angle U is -9.46

Answer: Angle U is 41°Step-by-step explanation:Vertical angles have the measures so they will equal to each other.

Set them equal to each other and solve for x.

6x + 11 = 10x – 9 Add 9 to both sides

+9 + 9

6x + 20 = 10x

-6x -6x

20 = 4x Divide both sides by 4

x = 5

Now input x into the equations and solve for the measure.

6(5) + 11 = 30 + 11 = 41

10(5) – 9 = 50 – 9 = 41