Answer:
a = 91
Measure of Angle A is 121 degrees.
Measure of Angle B is 107 degrees.
Measure of Angle Y is 73 degrees.
Measure of Angle C is 59 degrees.
Explanation:
It's given that diagonal inscribed angles are supplementary, meaning they add up to 180 degrees. So to solve for a, you need to set it up like this:
a + 16 + a - 18 = 180
Add like terms:
2a - 2 = 180
Add 2 to both sides:
2a - 2 = 180
+ 2 + 2
__________
2a = 182
Divide by 2 on both sides:
a = 91
Now to get the angle measurements, all you need to do is plug in 91 for a, for example:
Angle A = a + 30
Angle A = 91 + 30
Angle A = 121
Now just do the same and plug in 91 for a, to solve for Angle B, C, and Y.