Final answer:
To find the measure of ZB, we solve for x using the property of complementary angles summing up to 90 degrees. Plugging x back into the expression for ZB, we calculate that the measure of ZB is 63°.
Step-by-step explanation:
The question involves finding the measure of angle ZB, given that angles ZA and ZB are complementary angles and their measurements in terms of x are provided. When two angles are complementary, their measures add up to 90 degrees. The measure of angle ZA is given as (x + 9)° and the measure of angle ZB is (72 - x)°, as 15 was subtracted from 72.
To find x, we use the fact that the sum of the measures of complementary angles is 90°:
- m∠ZA + m∠ZB = 90°
- (x + 9)° + (72 - x)° = 90°
- x + 9 + 72 - x = 90
- 81 = 90
- x = 90 - 81
- x = 9
Now that we have the value of x, we can find the measure of ZB by plugging x back into the expression for m∠ZB:
- m∠ZB = (72 - x)°
- m∠ZB = (72 - 9)°
- m∠ZB = 63°
Therefore, the measure of ZB is 63°.