Question

the pair of complimentary angles are in the ratio of 2:7 find the measure of each angle in detail ​

Answer 1

        $\text{The given ratio between complimentary angles is }2:7$

        $\text{Let the common factor be }x$

$\implies \: \text{The two angles are }2x \text{ and }7x$

        $\text{Complimentary angles are those angles which sum upto }90^{\circ}$

$\implies \: 2x + 7x = 90$

$\implies \: 9x = 90$

$\implies \: x = \dfrac{90}{9}$

$\implies \: x = 10^{\circ}$

$\implies \: 2x = 2(10) = 20^{\circ}$

$\implies \: 7x = 7(10) = 70^{\circ}$

  $\therefore \; \; \boxed{\text{The two angles are }20^{\circ} \text{ and }70^{\circ}}$