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Svetlanka [38]
3 years ago
15

Find the value of the variables in each figure. Explain your reasoning.

Mathematics
1 answer:
sergiy2304 [10]3 years ago
4 0

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

-------------------------------------------------------------------

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

------------

2y and x are alternate angles and congruent , thus

2y = x = 30 ( divide both sides by 2 )

y = 15

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