Answer:
m∠XOY = 80°
Explanation:
We can make use of the fact that an exterior angle of a triangle is equal to the sum of the remote interior angles. The two angles marked with measures are exterior angles, so we can write the relations ...
132° = O +b
120° = O +a
Subtracting the second equation from the first, we get ...
(132°) -(120°) = (O +b) -(O +a)
12° = b -a
We observe that b:a = 13:10, a difference of 13-10 = 3 ratio units. Then each of those ratio units must stand for 12°/3 = 4°. The values of 'a' and 'b' are then ...
a : b = 10 : 13 = 40° : 52° . . . . . multiply ratio units by 4°, note b-a = 12°
Using the value for 'a' in the second of the original equations, we find ...
120° = O +40° . . substitute 40° for 'a'
80° = O . . . . . . . subtract 40°
The measure of angle XOY is 80°.