Question

If angle A and B are complementary and `A=5x+8` and `B=x+4`, what are the measurements of each angle?

Answer 1

A=73
B=17

Explanation:

If angles are complementary, then they are found adjacent to each other in a right angle.

![https://useruploads.socratic.org/HqA6lzi3Ste1L44SSGY0_complementary_angle.jpg)

From above, you can see that A+B=90

So I can add my two angles together and have it equal to 90

`(5x+8)+(x+4)=90`
`5x+8+x+4=90`
`6x+12=90`
`6x=90-12`
`6x=78`
`x=13`

So `A=5x+8=5(13)+8=65+8=73`
and `B=x+4=13+4=17`

Just to make sure you are correct, add your A and B together and they should equal to 90

ie `A+B=73+17=90`

Answer 2

`color(purple)(hat A = 73^@, color(brown)(hat B = 17^@`

Explanation:

If two angles are to be complementary, thier sum equals `90^@`

`hat A + hat B = 90^@`

`hat A = 5x + 8, hat B = x + 4`

`:. 5x + 8 + x + 4 = 90^@`

`6x = 90 - 12 = 78`

`x = 13`

`color(purple)(hat A = 5x + 8 = 73^@`

`color(brown)(hat B = x + 4 = 13 + 4 = 17^@`