Question

An angle less than 20° its complement . Find the measurments of the angle

Answer 1

$\textbf{\underline{Answer :-}}$

One Angle measures 55° and another measures 35°

$\textbf{\underline{Explanation :-}}$

$\textsf{\underline{Given :}}$

One angle = 20° less than another angle.

$\textsf{\underline{To find :}}$

The measures of the angles

$\textsf{\underline{Solution :}}$

As we know complementary angles are the angles which add up and make 90°

Consider one Angle as x

Consider second angle as x - 20

Equation =

$\tt{\implies \: x + x - 20 \: = 90}$

$\tt{\implies2x - 20 = 90}$

$\tt{\implies2x = 90 + 20}$

$\tt{\implies2x = 110}$

$\tt{\implies \: x = \dfrac{110}{2} }$

$\tt{\implies \: x = 55}$

Therefore one angle is 55°

Second angle = x - 20

$\tt{\implies \: x - 20}$

$\tt{\implies55 - 20}$

$\tt{\implies \: 35}$

Therefore another angle is 35°

$\textbf{\underline{Verification :-}}$

$\tt{\implies \: x + x - 20 = 90}$

$\tt{\implies55 + 55 - 20 = 90}$

$\tt{\implies110 - 20 = 90}$

$\tt{\implies90 = 90}$

$\therefore$LHS = RHS

$\therefore$One Angle measures 55° and another measures 35°

Answer 2

Two Angles which When added it become 90° called Complementary Angle.

Let one=x°

And Another is 20° less.

Then Other=(x-20)°

It when Added =90°

$\mathsf{x+(x-20)=90}$

$\mathsf{x+x-20=90}$

$\mathsf{x+x=90+20}$

$\mathsf{2x=110}$

$\mathsf{x=\frac{110}{2}}$

$\mathsf{x=55}$

We get x=55°

Other is 20° less

Other=x-20=55-20=35°

1st Angle=55°
2nd Angle=35°