Find the measure of each acute angle in a right triangle where the measure of one acute angle is 3 times the sum of the measure of the other acute angle and 8.

Answer 1

a + b = 90

a = 3(b + 8)

Substitute:

3(b + 8) +b = 90

3b + 24 + b = 90

4b = 66

b = 16.5

a = 73.5

Answer 2

x = 3y + 8

x + y = 90, y = 90 - x

Substitute:

x = 3(90 - x) + 8

x = 270 - 3x + 8

4x = 278

x = 69.5

y = 20.5

Answer 3

x = 3y + 8

x + y = 90, x = 90 - y

90 - y = 3y + 8

-4y = -82

y = 20.5

x = 69.5