Question

How do i solve for this?

Answer 1

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