Question

Two angles are making a linear pair. If one of them is one-third of the other, then find the angles.

Answer 1

Let one angle be x. It is given that the other angle is one-third of first.
So, other angle will be $\frac{1}{3}x$.
Again given that both the angle are making a linear pair so their sum will be ${180}^{\circ }$
$\therefore x+\frac{1}{3}x={180}^{\circ }\Rightarrow \frac{3x+x}{3}={180}^{\circ }\Rightarrow \frac{4x}{3}={180}^{\circ }\Rightarrow x=\frac{{180}^{\circ }\times 3}{4}\Rightarrow x={135}^{\circ }$
Hence, the angles are ${135}^{\circ }and\frac{1}{3}\times {135}^{\circ },i.e.{135}^{\circ }and{45}^{\circ }$