Question

What is the measure of two complementary angles if the measure of the larger angles is 12 more than twice the measure at the smaller angle?

Answer 1

The smaller angle is `26^@`
The larger angle is `64^@`

Explanation:

Let `x` equal the number of degrees in the smaller angle.

Smaller angle. . . . . . . . . . `x` `larr` smaller angle
Twice that measure . . . `2x`
12 more than that . . . . . `2x + 12` `larr` larger angle

Together, these two angles add up to `90^@`

[small angle] plus [large angle ] `= 90`
`[ . . . ( x ) . . .] . + . [ .(2x + 12) ] = 90`

`(x) + (2x + 12) = 90`
Solve for `x`, already defined as "the number of degrees in the smaller angle."

1) Combine like terms
`3x + 12 = 90`

2) Subtract 12 from both sides to isolate the `3x` term
`3x = 78`

3) Divide both sides by `3` to isolate `x`, already defined as "the number of degrees in the smaller angle"
`x = 26` `larr` the number of degrees in the smaller angle

Answer:
The smaller angle is `26^@`
So the larger angle must be `64^@`

Check
`26` plus `12` more than (`2` times `26`) should equal `90`
`26 + 2(26) + 12` should equal `90`
`26 + 52 + 12` should equal `90`
`26 + 64` should equal `90`
`90` does `= 90`
Check!