Question

An angle is $\frac{2}{5}$ of its supplement. What is the degree measure of the angle?

Answer 1

Let the measure of the angle $=x^{\circ }$

then its supplement $=(180-x{)}^{\circ }$

Now angle is $\frac{2}{5}$ of its supplement.

that is,

$x=\frac{2}{5}({180}^0-x)$

$x=\frac{2}{5}\times {180}^0-\frac{2}{5}x$

$x+\frac{2}{5}x={72}^0$

$\frac{7}{5}x={72}^0$

$x=\frac{72\times 5}{7}={\frac{360}{7}}^{\circ }$