Question

The sum of the measures of two complementary angles is 90. If one angle measure 9 more than twice the other, what are the measures of the angles?

Answer 1

`27˚,63˚`

Explanation:

`angle1` and `angle2` are complementary if

`color(white)(xx)mangle1+mangle2=90`

We know that:

`color(white)(xx)mangle1=x`
`color(white)(xx)mangle2=2x+9`

Thus,

`color(white)(xx)x+(2x+9)=90`
`color(white)(xx)3x+9=90`
`color(white)(xx)3x=81`
`color(white)(xx)x=27`

`mangle1=x=27`
`mangle2=2x+9=2(27)+9=63`

The two complementary angles are `27˚` and `63˚`.