Question

The difference of two complementary angles is 70 degrees. Find the measures of the angles.

Answer 1

We know, sum of complementary angles = 90°

Let, one of the angle = x°

∴ Another angle = (90 - x)°

As per condition,

(x°) - (90 - x)° = 70°

⇒ x° - 90° + x° = 70°

⇒ 2x° = 70° + 90° = 160°

⇒ x° = 80°.

So, angles are:-

1. x° = 80°
2. (90 - x)° = (90 - 80)° = 10°.

Answer 2

`80`° and
`10`°

Explanation:

Complementary angles are a pair of angles whose measures have a sum of
`90`°. Therefore, if we let the measure of the bigger angle be
`x`, then the measure of the smaller angle will be
`x-70` because we are given that the difference of the measures of the two angles is
`70`°. We can write the following equation to solve for
`x`:

`x+x-70=90`

Solving for
`x`, we get:

`x+x-70=90`

`2x-70=90` (Simplify LHS)

`2x-70+70=90+70` (Add
`70` to both sides of the equation to isolate
`x`)

`2x=160` (Simplify)

`(2x)/(2)=(160)/(2)` (Divide both sides of the equation by
`2` to get rid of
`x`'s coefficient)

`x=80` (Simplify)

Therefore, the measure of one angle is
`80`° and the measure of the other angle is
`x-70=80-70=10`°. Hope this helps!