Answer:
see explanation
Step-by-step explanation:
(16)
The mid segment ZW is half the sum of the parallel bases
ZW = [tex]\frac{38+20}{2}[/tex] = [tex]\frac{58}{2}[/tex] = 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)
[tex]\frac{UV+XY}{2}[/tex] = ZW
[tex]\frac{3x-1+7x+1}{2}[/tex] = 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
