Question

Question 18

The difference fo two complementary angles is ${30}^{\circ }.$ Then the angles are
(a) ${60}^{\circ },{30}^{\circ }$
(b) ${70}^{\circ },{40}^{\circ }$
(c) ${20}^{\circ },{50}^{\circ }$
(d) ${105}^{\circ },{75}^{\circ }$

Answer 1

Let one of the angles be x. Since, the difference between the two angles is ${30}^{\circ }$, then the other angle will be $(x-{30}^{\circ })$.
Also, the two angles are complementary , so their sum is equal to ${90}^{\circ }$.
$\therefore x+(x-{30}^{\circ })={90}^{\circ }\Rightarrow x+x-{30}^{\circ }={90}^{\circ }\Rightarrow 2x={90}^{\circ }+{30}^{\circ }\Rightarrow 2x={120}^{\circ }\Rightarrow x=\frac{{120}^{\circ }}{2}\Rightarrow x={60}^{\circ }$

$\therefore {\text{Required angles are 60}}^{\circ }\text{and}({60}^{\circ }-{30}^{\circ }),\text{i.e.}{60}^{\circ }\text{and}{30}^{\circ }$.