Answer:
M<3 is 49 degrees, M<4 is 131 degrees
Step-by-step explanation:
This is a case of supplementary angles. M<1 and M<2 are supplementary, which means that their angle degrees added together will be equal to 180. The same is for M<2 and M<3, and M<3 and M<4, and M<1 and M<4. Basically, two angles are supplementary when they form a straight line, or 180 degrees
First, we know that M<1 and M<2 added together is 180. We know M<1 is 11x-38 and M<2 is 19x+8, so then, we have:
(11x-38) + (19x+8) = 180
30x - 30 = 180
30x = 210
x = 7
Now, we plug in 7 for x to find M<1 and M<2.
M<1 is (11x-28), so it would be 49 degrees.
M<2 is (19x+8), so it would be 131 degrees (or just do 180-49).
Now, we can find M<3 and M<4 easily. M<3 and M<2 are supplementary, so 131 + M<3 must equal 180. Thus, M<3 is 49.
M<4 and M<1 are supplementary, so 49 + M<4 must equal 180. Thus, M<3 is 131.
<u>AN EASIER WAY TO FIND M<3 AND M<4:</u>
Vertical angles are angles directly opposite each other, created by two intersecting lines. A pair of vertical angles holds the same degree measurements. In this problem, M<2 and M<4 are a pair of vertical angles, and M<3 and M<1 are a pair. Thus, M<2 and M<4 must are the same degree and M<3 and M<1 must are the same degree. Thus, if M<2 is 131, M<4 is 131 degrees as well. If M<1 is 49 degrees, M<3 is 49 degrees as well.
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