Answer:
If ZA and ZB are supplementary angles, then their measures add up to 180 degrees. So we can represent ZA as x and ZB as y.
According to the given information, the measure of ZB is 33° more than half the measure of ZA. So we can represent this as:
y = (1/2)x + 33
And since ZA and ZB are supplementary, we can express the relationship between the two angles as:
x + y = 180
Now we have a system of two equations with two variables:
y = (1/2)x + 33
x + y = 180
We can solve for x and y using these equations.
First, we substitute the first equation into the second equation:
x + ((1/2)x + 33) = 180
Simplifying:
x + (1/2)x + 33 = 180
x + (1/2)x = 180 - 33
x + (1/2)x = 147
Combining like terms:
(3/2)x = 147
Dividing both sides by 3/2
x = 98
Now we can substitute this value back into the first equation to find the measure of ZB:
y = (1/2)x + 33
y = (1/2)(98) + 33
y = 49 + 33
y = 82
So the measure of ZA is 98°, and the measure of ZB is 82°.
Explanation: