Question

Can someone pls pls pls answer these two questions for me, I need to finish my assignment and I'm stuck on these 2.

1. Suppose that m∠ABC = 163° and m∠XYZ = 5x + 2. If ∠ABC and ∠XYZ are supplementary angles, determine the value of x.


2. ∠X and ∠Y form a linear pair. If the measure of ∠X equals 24x − 36° and the measure of ∠Y equals 12x, how much is x?

Answer 1

Problem 1

Answer: x = 3

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Step-by-step explanation:

Angles ABC and XYZ are supplementary. By definition, they can be glued together to form a straight line of 180 degrees.

(angle ABC)+(angle XYZ) = 180

(163)+(5x+2) = 180

5x+165 = 180

5x = 180-165

5x = 15

x = 15/5

x = 3

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Problem 2

Answer: x = 6

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Step-by-step explanation:

This is similar to problem 1. A linear pair of angles are always supplementary. More specifically, a linear pair of angles are supplementary and they are adjacent as well.

Add up the angles, set the sum equal to 180, and solve for x.

(angleX) + (angleY) = 180

(24x-36) + (12x) = 180

36x-36 = 180

36x = 180+36

36x = 216

x = 216/36

x = 6