Question

One of the exterior angle 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

Sum of interior opposite angle is equal to the exterior angle

Given exterior angle$={80}^{\circ }$ and interior angle ratio is $(3:5)$

Let the angles be $x3x,5x$

$3x+5x=80;8x=80;x={10}^o$

$\therefore {30}^o\&{50}^o$ are interior opposite angles

$30+50+A=180$ [Sum of angles in a triangle is ${180}^o$]

$A={100}^o$

$A={100}^o,B={30}^o,C={50}^o$ are angles of triangle.