Problem
GEO-B1-M01-P004 An Exterior Angle
#4
★☆☆☆☆ Level 1 of 5
In triangle \(ABC\), the exterior angle at \(C\) is \(126^\circ\), and \(\angle A=49^\circ\). Find \(\angle B\) and \(\angle C\).
An exterior angle equals the sum of the two non-adjacent interior angles.
We have \(126^\circ=\angle A+\angle B\), so \(\angle B=126^\circ-49^\circ=77^\circ\). The interior angle at \(C\) is adjacent to the given exterior angle, hence \(\angle C=180^\circ-126^\circ=54^\circ\).
Checks the distinction between an exterior angle and the interior angle at the same vertex.