Question

in triangle ( abc ), the measure of angle ( a ) is ( 40.5^circ ) and the measure of an exterior angle at ( b ) is ( 96.3^circ ). what is the measure of angle ( c )?
( 136.8^circ )
( 40.5^circ )
( 96.3^circ )
( 55.8^circ )

Explanation:

Step1: Find interior angle at B

An exterior angle and its adjacent interior angle are supplementary (sum to \(180^\circ\)). So, interior angle at \(B = 180^\circ - 96.3^\circ = 83.7^\circ\).

Step2: Use triangle angle sum

The sum of angles in a triangle is \(180^\circ\). So, \(\angle A + \angle B + \angle C = 180^\circ\). Substitute \(\angle A = 40.5^\circ\) and \(\angle B = 83.7^\circ\): \(\angle C = 180^\circ - 40.5^\circ - 83.7^\circ = 55.8^\circ\).

Answer:

\(55.8^\circ\) (the option with \(55.8^\circ\))