Answer:
Y ≈ 47.47°
Step-by-step explanation:
The exterior angle (W) is equal to the sum of the remote interior angles (X, Y). Since X=Y, we have ...
W = X + Y
W = X +X = 2X . . . . substitute X for Y
17x +18.2 = 2(5x +24.9)
17x +18.2 = 10x +49.8 . . . . . . . eliminate parentheses
7x = 31.6 . . . . . . . . . . . . . subtract 18.2
x = 4 18/35 ≈ 4.51 . . . . . divide by 7
Then the values of angle y is ...
Y = 5x +24.9 ≈ 5(4.5143) +24.9
Y ≈ 47.47°
_____
Additional comment
Angle X is the same as angle Y, 47.47°. Angle W will be twice this, 94.94°, and angle Z will be the supplement of this value, 85.06°.
