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

Given:

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

To do:

We have to find the angles.

Solution:

Let the larger angle be x.

This implies,

Smaller angle $= x-18°$

We know that,

Supplementary angles add up to 180°.

Therefore, 

$x + x -18°  =  180°$

$2x - 18° = 180°$

$2x  =  180° + 18°

$2x  =  198°$

$x  = \frac{198°}{2}$

$x  =  99°$

$x - 18°  =  99° - 18°  =  81°$

The larger angle is 99° and the smaller angle is 81°.

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Updated on: 10-Oct-2022

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