Question

`/_DEF` and `/_ABC` are complementary angles? `/_ ABC` is nine times as large as `/_DEF`. What is the measure of each angle?

Answer 1

`angleABC=81˚,angleDEF=9˚`

Explanation:

The angles are complementary, which means the following statement is true:

`mangleABC+mangleDEF=90color(white)(sssss)` (i)

Since `angleABC` is `9` times greater than `angleDEF`,

`mangleABC=9(mangleDEF)color(white)(sssss)` (ii)

Replace `mangleABC` with `9(mangleDEF)` in (i).

`9(mangleDEF)+mangleDEF=90`
`rArr 10(mangleDEF)=90`
`rArr mangleDEF=9`

Since `mangleABC=9(mangleDEF),` `mangleABC=9(9)=81`.