Question

Two angles are complementary. The measure of the larger angle is 10 more than 4 times the measure of the small angle. Find the measures of both angles.

Answer 1

`a=16`

`b=74`

Explanation:

If two angles are complementary to each other, then their sum is 90 degrees.

So we have:
`a+b=90`.

Let's say
`b` is the larger of the two.

We have that
`b` is 10 more than 4 times the measure of
`a`.

An equation this is:
`b=10+4a`.

So I'm going to plug second equation into first equation:

`a+b=90` with
`b=10+4a`:

`a+(10+4a)=90`

Combine like terms:

`5a+10=90`

Subtract 10 on both sides:

`5a=80`

Divide both sides by 5:

`a=(80)/(5)`

Simplify:

`a=16`

Now to find
`b`:

`b=10+4a` with
`a=16`:

`b=10+4(16)`

`b=10+64`

`b=74`

Answer 2

Explanation:

Let the measurement of the smaller angle = x

Larger angle = 4x + 10

x + (4x + 10) = 90 {complementry}

5x + 10 = 90

5x = 90 -10

5x = 80

x = 80/5

x = 16

Smaller angle = 16

Larger angle = 4*16 + 10 = 64+10 = 74