Question

Suppose ∠A and ∠B are complementary angles, m∠A = (3x + 5)°, and

m∠B = (2x – 15)°. Solve for x and then find m∠A and m∠B.

Answer 1

m∠A + m∠B = 90


`(3x + 5) + (2x - 15) = 90`


`(3x + 2x) + (5 - 15) = 90`


`5x - 10 = 90`


`5x - 10 +10 = 90+10`


`5x = 100`


`5x/5 = 100/5`
`Divide \ both \ sides \ by \ 5`


`x = 20`
`Solutions`

m∠A =
`3x + 5`
`(x=20)`

m∠A =
`3(20) + 5`
`Substitute \ x \ for \ 20`

m∠A =
`60 + 5`
`Simplify`

m∠A =
`65`


m∠B =
`2x - 15`

m∠B =
`2(20) - 15`

m∠B =
`40 - 15`

m∠B =
`25`

Answer 2

m∠A + m∠B = 90
(3x + 5) + (2x - 15) = 90
(3x + 2x) + (5 - 15) = 90
5x - 10 = 90
+ 10 + 10
5x = 100
5 5
x = 20

m∠A = 3x + 5
m∠A = 3(20) + 5
m∠A = 60 + 5
m∠A = 65

m∠B = 2x - 15
m∠B = 2(20) - 15
m∠B = 40 - 15
m∠B = 25