Question

One of the exterior angles of a triangle is ${80}^{\circ }$ and the interior opposite angles are in the ratio of $3:5$. Find the angles of the triangle.

Answer 1

Given: Exterior angle $={80}^{\circ }$

Ratio of opposite interior angles $=3:5$

Let the interior angles be $3x$ and $5x$

$\Rightarrow 80=3x+5x$ [Exterior angle is equal to the sum of interior opposite angles.]

$\Rightarrow 80=8x$

$\Rightarrow x=10$

The two interior angles are $3\times 10={30}^{\circ },$ and $5\times 10={50}^{\circ }$

The other angle $=180-(30+50)=100$ [Angle sum Property]

Hence, all three angles of the given triangle are ${30}^{\circ },{50}^{\circ },{100}^{\circ }$