Question

If two supplementary angles differ by ${40}^{\circ }$, then find the angles.

• A. ${90}^{\circ },{130}^{\circ }$
• B. ${60}^{\circ },{120}^{\circ }$
• C. ${70}^{\circ },{110}^{\circ }$
• D. ${50}^{\circ },{90}^{\circ }$

Answer 1

The correct option is C ${70}^{\circ },{110}^{\circ }$

Let one angle be $x$.
Then, the other angle is $x-{40}^{\circ }$.

We know that, sum of two supplementary angles is ${180}^{\circ }.$

Hence,
$x+(x-{40}^{\circ })={180}^{\circ }2x-{40}^{\circ }={180}^{\circ }2x={180}^{\circ }+{40}^{\circ }2x={220}^{\circ }x=\frac{{220}^{\circ }}{2}x={110}^{\circ }$

$\therefore$ Other angle $=x-40=110-40={70}^{\circ }$

Thus, the angles are ${70}^{\circ }$ and ${110}^{\circ }$.