Question

An exterior angle of a triangle is ${108}^{\circ }$ and its its ineterior opposite angles are in are in the ratio 4 : 5 . The triangle are

Answer 1

In $\Delta ABC,BC$ is produced to D and $\angle ACD={108}^{\circ }$

Ratio in $\angle A:\angle B=4:5$

$\because$ Exterior angle of a triangle is equal to the sum of its opposite interior angles

Ratio in$\angle ACD=\angle A+\angle B={108}^{\circ }$

$\angle A=\frac{{108}^{\circ }\times 4}{4+5}=\frac{{108}^{\circ }\times 4}{9}={48}^{\circ }$

$\angle B=\frac{{108}^{\circ }\times 5}{9}={60}^{\circ }$

$\therefore \angle C={180}^{\circ }-(A+B)$

=$({180}^{\circ }-{108}^{\circ })={72}^{\circ }$

$\therefore$ Angles are ${48}^{\circ },{60}^{\circ },{72}^{\circ }$