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

Answer:

$80$° and $10$°

Step-by-step 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)

$\frac{2x}{2}=\frac{160}{2}$ (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!