Question

The larger of the two supplementary angles exceeds the smaller by 18°. Find them​

Answer 1

Answer:

Let Larger angle be x

& Smaller angle be y

Given that

Larger angle exceeds Smaller angle by 18°

x - y = 18

(1)

Also both angles are supplementary

Sum of both angles = 180°

x + y = 180

Thus, our equations are

x-y = 18

x + y = 180

From (1)

x - y = 18

x = 18+ y

Substituting x in (2)

x + y = 180

(18+ y) + y = 180

18+ y + y = 180

18+ 2y = 180

...(1)

...(2)

...(2)

2y = 180-18

2y = 162

162 y = = 81

Putting y = 81 in (1).

x-y = 18

x-81 = 18

x = 18 + 81

x = 99

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Hence, x = 99 and y = 81

Thus,

Larger Angle = x = 99°

Smaller Angle = y = 81°