In triangleABC, the interior angle at A is 51^circ and the exterior angle at B is 119^circ. The interior angle at C measures what?

Apr 7, 2018

Interior angle at C measures ${68}^{\circ}$

Explanation:

In a triangle sum of all the interior angles is ${180}^{\circ}$

Now interior angle $\angle A = {51}^{\circ}$,

as exterior angle $B = {119}^{\circ}$, interior angle is ${180}^{\circ} - {119}^{\circ} = {61}^{\circ}$

Hence interior angle at $C$ measures ${180}^{\circ} - {51}^{\circ} - {61}^{\circ} = {68}^{\circ}$

Alterative method

As any exterior angle is equal to sum of both the interior opposite angles, exterior angle at $B$ is equal sum of interior anglesat $A$ and $C$

hence ${119}^{\circ} = {51}^{\circ} + m \angle C$

and $m \angle C = {119}^{\circ} - {51}^{\circ} = {68}^{\circ}$