1) Given that MN is the midsegment, it means that
MN = 1/2(WZ + XY)
MN = 1/2(11 + 3) = 1/2 * 14
MN = 7
2) The base angles are congruent. This means that
angle WZN = angle XWZ = 78
The top angles are equal. The sum of the base angles is 78 + 78 = 156
Since the sum of all the angles is 360, the sum of each top angle is
(360 - 156)/2 = 102 degrees. This means that
angle WXY and angle ZYX = 102
Angle XMN and angle XWN are congruent. This is because they are corresponding angles. thus,
angle XMN = 78 degrees
3) Recall, MN = 1/2(WZ + XY)
If MN = 10 and WZ = 14, then
10 = 1/2(14 + XY)
10 * 2 = 14 + XY
20 = 14 + XY
XY = 20 - 14
XY = 6
4) Recall that angle MWZ = angle WZN because they are the base angles. Given that angle MWZ = 15x - 5 and angle WZN = 90 - 4x, it means that
15x - 5 = 90 - 4x
15x + 4x = 90 + 5
19x = 95
x = 95/19
x = 5
