Answer:
Step-by-step explanation:
Remark
No wonder you are posting this. You should never have to rely on a diagram to get an answer, and this diagram is particularly unreliable. What exactly does the peak mean? Does it tell you that the peak is both y and 20 degrees? I'm going to assume so. But it is a very shakey assumption.
Pick a triangle with 2 ys in it. The third angle hits one of the sides of the triangle. Every triangle has 180 degrees. The top angle is 20 degrees and all ys therefor are 20 degrees. So the third angle is y + y + x =180
The 2xs are in a quadrilateral near the top. All quadrilaterals have 360 degrees. q and one of the angles are vertically opposite. q is then known.
Givens
y = 20
third angle = x
solution
triangles with 2 ys (isosceles)
y + y + x = 180
2y + x = 180
y = 20
2*20 + x = 180
40 + x = 180
x = 140
Quadrillateral
140 + 140 + 20 + vertically opposite q = 360
300 + vertically opposite q = 360
vertically opposite q = 360 - 300
vertically opposite q = 60
Answer
q = 60
