Question

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?

Answer 1

Interior angle at C measures `68^@`

Explanation:

In a triangle sum of all the interior angles is `180^@`

Now interior angle `/_A=51^@`,

as exterior angle `B=119^@`, interior angle is `180^@-119^@=61^@`

Hence interior angle at `C` measures `180^@-51^@-61^@=68^@`

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^@=51^@+m/_C`

and `m/_C=119^@-51^@=68^@`