Answer:
see explanation
Step-by-step explanation:
The figure has one pair of parallel sides and is a trapezoid.
Each lower base angle is supplementary to the upper base angle on the same side, thus
15x + 30 + 10x = 180 , that is
25x + 30 = 180 ( subtract 30 from both sides )
25x = 150 ( divide both sides by 25 )
x = 6
Also
3y + 18 + 90 = 180 , that is
3y + 108 = 180 ( subtract 108 from both sides )
3y = 72 ( divide both sides by 3 )
y = 24
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2x, 90 and x lie on a straight line and sum to 180 , thus
2x + 90 + x = 180 , that is
3x + 90 = 180 ( subtract 90 from both sides )
3x = 90 ( divide both sides by 3 )
x = 30
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2y and x are alternate angles and congruent , thus
2y = x = 30 ( divide both sides by 2 )
y = 15
