Question

An exterior angle of triangle is ${110}^0$. If one of the interior opposite angles is ${30}^0$, then the other two angles of the triangle are

• A. ${40}^0,{110}^0$
• B. ${50}^0,{100}^0$
• C. ${60}^0,{90}^0$
• D. ${70}^0,{80}^0$

Answer 1

The correct option is D ${70}^0,{80}^0$

Given:Exterior angle is${110}^{\circ }$;Interior opposite angle is ${30}^{\circ }.$

To find:O\quad two\quad angles\quad of\triangle gle.$

$Solution:\angle BCA+\angle ACK={180}^{\circ }\left(Linesegmentangle\right)$

$\therefore \angle BCA+110={180}^{\circ }$

$\therefore \angle BCA={70}^{\circ }$

$\angle ABC+\angle BAC=\angle ACK$

(Exterior angle is sum of opposite interior angles)

$\therefore 30+\angle BAC=110$

$\angle BAC={80}^{\circ }$