Question

In a triangle, an exterior angle at a vertex is ${95}^{\circ }$ and its one of the interior opposite angle is ${55}^{\circ }$ then the measure of the other interior angle is

• A. ${55}^{\circ }$
• B. ${85}^{\circ }$
• C. ${40}^{\circ }$
• D. ${9.0}^{\circ }$

Answer 1

The correct option is C

${40}^{\circ }$

In $\Delta ABC,BA$ is produced to D such that $\angle CAD={95}^{\circ }$

and let $\angle C={55}^{\circ }$ and $\angle B=x^{\circ }$

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

$\therefore \angle CAD=\angle B+\angle C$

$\Rightarrow {95}^{\circ }=x+{55}^{\circ }$

$\Rightarrow x={95}^{\circ }-{55}^{\circ }={40}^{\circ }$

$\therefore$ Other interior angle =${40}^{\circ }$