Question

Find the angles in each of the following:
(a) The angles are complementary and the smaller is 40° less than the larger.
(b) The angles are complementary and the larger is four times the smaller.
(C) The angles are supplementary and the smaller is one-half of the larger.​

Answer 1

Step-by-step explanation:

i)If angles are complementary then their sum should be 90

∘

.

As per the given condition if smaller angle is X then the larger angle should be X+40

∘

,

Now,

X+X+40

∘

=90

∘

,

2X=50

∘

,

X=25

∘

Hence, smaller angle is 25

∘

and larger angle is 65

∘

.

ii)If angles are complementary then their sum should be 90

∘

.

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

Now,

X+4X=90

∘

,

5X=90

∘

,

X=18

∘

Hence, smaller angle is 18

∘

and larger angle is 72

∘

.

iii)If angles are supplementary then their sum should be 180

∘

.

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

Now,

X+2X=180

∘

,

3X=180

∘

,

X=60

∘

Hence, smaller angle is 60

∘

and larger angle is 120

∘

.