Question

ZA and ZB are complementary angles. If mZA = (x + 2)° and mLB = (x - 26)°, then find the measure of ZA. a) 28° b) 48° c) 76° d) 104°

Answer 1

To find the measure of angle ZA, set up and solve an equation using the fact that ZA and ZB are complementary angles. The measure of ZA is 59 degrees.

Step-by-step explanation:

To find the measure of angle ZA, we need to use the fact that ZA and ZB are complementary angles. Complementary angles add up to 90 degrees. So we can write an equation:

(x + 2) + (x - 26) = 90

Simplifying the equation, we get:

2x - 24 = 90

Adding 24 to both sides, we have:

2x = 114

Dividing both sides by 2, we find:

x = 57

Finally, we substitute this value back into the expression for ZA:

mZA = (x + 2) = (57 + 2) = 59 degrees

Learn more about Complementary angles