Question

Find the angles in each of the following.
i) The angles are complementary and the smaller is ${40}^0$ less than the larger.
ii) The angles are complementary and the larger is four times the smaller,
iii) The angles are supplementary and the smaller is one- half of the larger.

Answer 1

$i)$If angles are complementary then their sum should be ${90}^{\circ }$.

As per the given condition if smaller angle is $X$ then the larger angle should be $X+{40}^{\circ }$,

Now,

$X+X+{40}^{\circ }={90}^{\circ }$,

$2X={50}^{\circ }$,

$X={25}^{\circ }$

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

$ii)$If angles are complementary then their sum should be ${90}^{\circ }$.

As per the given condition if smaller angle is $X$ then the larger angle should be $4X$,

Now,

$X+4X={90}^{\circ }$,

$5X={90}^{\circ }$,

$X={18}^{\circ }$

Hence, smaller angle is ${18}^{\circ }$ and larger angle is ${72}^{\circ }.$

$iii)$If angles are supplementary then their sum should be ${180}^{\circ }$.

As per the given condition if smaller angle is $X$ then the larger angle should be $2X$,

Now,

$X+2X={180}^{\circ }$,

$3X={180}^{\circ }$,

$X={60}^{\circ }$

Hence, smaller angle is ${60}^{\circ }$ and larger angle is ${120}^{\circ }.$