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balandron [24]
2 years ago
8

How do i solve for this?

Mathematics
1 answer:
vodka [1.7K]2 years ago
5 0

Answer:

see explanation

Step-by-step explanation:

(16)

The mid segment ZW is half the sum of the parallel bases

ZW = \frac{38+20}{2} = \frac{58}{2} = 29

(17)

The lower base angles are congruent , so

∠ UYX = ∠ VXY = 35°

(18)

Any lower base angle is supplementary to any upper base angle , then

∠ VUY = 180° - ∠ UYX = 180° - 35° = 145°

(19)

\frac{UV+XY}{2} = ZW

\frac{3x-1+7x+1}{2} = 10 ( multiply both sides by 2 to clear the fraction )

10x = 20 ( divide both sides by 10 )

x = 2

Then

XY = 7x + 1 = 7(2) + 1 = 14 + 1 = 15

(20)

The legs are congruent , so

UY = VX

5a - 6 = 3a + 2 ( subtract 3a from both sides )

2a - 6 = 2 ( add 6 to both sides )

2a = 8 ( divide both sides by 2 )

a = 4

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