Question

The measure of angle x is 25 more than 4 times the measure of its complement. Find the measure of x.

Answer 1

- Two angles that are complements of each other add to equal 90 degrees (they are complementary angles). 
- One angle measures x degrees.
- The other angle measures 25 more than 4 times the angle that measures x degrees; it measures 4x + 25 degrees.

To find x, set the sum of these expressions (x and 4x + 25) equal to 90 and solve algebraically for x.

90 = x + (4x + 25)
90 = x + 4x + 25
90 = 5x + 25
65 = 5x
13 = x

If you wanted to find the measure of angle x, you'd substitute 13 for x in its expression, 4x + 25.

4x + 25
4(13) + 25
52 + 25
77

Answer:
x = 13
m∠x = 77°