Question

The supplementary angle of an angle is one third of the angle. Then the angle and its supplement are __________.

• A. ${135}^o,{45}^o$
• B. ${60}^o,{180}^o$
• C. ${120}^o,{350}^o$
• D. ${60}^o,{120}^o$

Answer 1

Answer: (A)

${135}^o,{45}^o$

Let the angle is $x$, and its supplementary angle is $\frac{1}{3}x$.

We know that the sum of the supplementary angles is ${180}^o$, then

$x+\frac{1}{3}x={180}^o\Rightarrow \frac{4}{3}x=180$

$\Rightarrow x=\frac{180\times 3}{4}={135}^o$

It's supplementary angle $=\frac{135}{3}={45}^o$