Question

If ZA and B are complements and the measure of ZA is 3 times its complement, then what is mZA?

Answer 1

To find the measure of angle ZA, we used the fact that ZA and its complement B add up to 90 degrees. The measure of ZA is three times that of B. Solving for the angles, the measure of ZA is found to be 67.5 degrees.

Step-by-step explanation:

When dealing with complementary angles, the sum of the measures of the two angles must equal 90 degrees. In this case, we have angle ZA and its complement B. Since the measure of ZA is 3 times its complement, we can set up the following algebraic equation:

Let mZA = 3x and mB = x, where x is the measure of the complement of ZA. Therefore:

mZA + mB = 90

3x + x = 90

4x = 90

x = 22.5

Since mZA is 3 times the measure of its complement, mZA = 3 * 22.5 = 67.5 degrees.