Answers:
x = 13
y = 24
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Explanation:
Refer to the diagram below.
The triangle has interior angles (7x-31), 63, and some unknown angle, which we'll call z. This angle z is congruent to (5x-8) as the angles are alternate interior angles.
Alternate interior angles are congruent when we have parallel lines like this.
So z = 5x-8
Add up the three angles inside the triangle, set the sum equal to 180, and solve for x
(angle1)+(angle2)+(angle3) = 180
(7x-31)+63+(5x-8) = 180
12x+24 = 180
12x = 180-24
12x = 156
x = 156/12
x = 13
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The angle z mentioned earlier is adjacent to the (4y+27) angle. These two angles form a straight line. They are considered a linear pair. This means they are supplementary (they add to 180)
z+(4y+27) = 180
(5x-8)+(4y+27) = 180
5x + 4y + 19 = 180
5(13) + 4y + 19 = 180
65 + 4y + 19 + 180
4y + 84 = 180
4y = 180-84
4y = 96
y = 96/4
y = 24
