Answer:
10
Explanation:
I have labeled the three rays which intersect as AB, CD and EF for ease of explanation. The intersection point is labeled O
∠EOD = y° since these are vertically opposite angles
Since rays AB and CD intersect at right angles, ∠AOC = 180° - ∠AOD and since ∠AOD is given as 90°, ∠AOC = 180 - 90 = 90°
But ∠AOC = ∠AOE + ∠EOC = x + y
So we have x + y = 90 ..............(1)
By similar reasoning ∠DOF which is y° + ∠FOB = 90°
∠FOB = 2x - 80
So y + 2x - 80 = 90
or y + 2x = 90 + 80
y + 2x = 170
2x + y = 170 ..........(2)
Writing these equations down we get
x + y = 90 ... (1)
2x + y = 170 ... (2)
Multiply equation (1) by 2 to get:
2(x + y) = 2 x 90
2x + 2y = 180 ... (3)
(3) - (2) ==>
2x + 2y - (2x + y) = 180 - 170
2x + 2y - 2x - y = 10
2y - y = 10
or
y = 10