1.

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

Answer»

We know that two angles are supplementary angles if their sum is 180°.

Let smaller angle is x°. 

Given that difference between supplementary angles are 18° 

Therefore, the other angle is x° + 18°. 

Hence, x° & x° + 18° are supplementary angles. 

Therefore, x° + x° + 18° = 180°. (By definition of supplementary angles) 

⇒ 2 x° + 18° = 180°⇒ 2x° = 180° – 18° = 162° 

⇒ x° = \(\frac{162°}{2}\) = 81°. 

And x° + 18° = 81°+18° = 99°. 

Hence, the angles are 81°, 99°



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