Question

Find the angles in each of the following.
(i) The angles are complementary and the smaller is ${40}^{\circ }$ less then the larger.

(ii) The angles are complementary and the larger is four times the smaller.

Answer 1

We know that

$\angle A+\angle B={90}^{\circ }$

Consider the given question,

(i) Let larger angle is $x^{\circ }$

then smaller angle is $(x-40{)}^{\circ }$

$x^{\circ }+{(x-40)}^{\circ }={90}^{\circ }$

$2x^{\circ }={130}^{\circ }$

$x^{\circ }={65}^{\circ }$

Smaller angle is ${65}^{\circ }$- ${40}^{\circ }$

$={25}^{\circ }$

Hence, larger angle is$x={65}^{\circ }$ and smaller angle is ${25}^{\circ }$

(ii) Let smaller angle is $x^{\circ }$

then, larger angle is $4x^{\circ }$

$x^{\circ }+4x^{\circ }={90}^{\circ }$

$5x^{\circ }={90}^{\circ }$

$x^{\circ }=18$

larger angle is $4\times {18}^{\circ }$

$={52}^{\circ }$

Hence,larger angle is ${52}^{\circ }$ and smaller angle is ${18}^{\circ }$