Question

Two angles are complementary. The larger angle is 3degree less than the twice the measure of the smaller angle. Find the measure of each angle.

Answer 1

$\bold{COMPLENTARY \: ANGLES}$

The pair if angles whose sum is 90 degress its called pair of complementary angles.

So if the angle A and angle B are complementary So,

$\mathsf{A + B = 90}$

let the smaller angle be x.

ACCORDING TO QEUSTION

larger angle is 3 less twice the smaller one.

so angle willl be $\mathsf{2x-3}$

Since, these are complementary so,

$\mathsf{x + 2x-3 = 90}$

$\mathsf{x+ 2x - 3 = 90}$

$\mathsf{3x -3 = 90}$

$\mathsf{3x = 90 + 3}$

$\mathsf{3x = 93}$

$\mathsf{x = \frac{93}{3}}$

$\huge \boxed{x = 31^{\circ}}$

So, the smaller angle is 31

So, the larger angle is twice three less than smaller one

So,

▶$\mathsf{2 \times 31 - 3)}$

▶$\mathsf{62-3}$

$\huge \boxed{Larger \: number = 59^{\circ}}$

So ,

$\underline \mathcal{Smaller number = 31^{\circ}}$

$\underline \mathcal{Larger number =59^{\circ}}$