Question

in △abc, m∠a = 35 and the measure of the exterior angle at c is 100. which is the longest side of the triangle?

Explanation:

Step1: Find the measure of $\angle ACB$

The exterior angle at \(C\) is \(100^{\circ}\). Using the exterior - angle property (an exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles), and the fact that the exterior angle and the interior angle at \(C\) are supplementary (\(\angle ACB+100 = 180\)). So, \(\angle ACB=180 - 100=80^{\circ}\).

Step2: Find the measure of $\angle B$

Using the triangle - angle sum property (\(\angle A+\angle B+\angle ACB = 180^{\circ}\)). Given \(\angle A = 35^{\circ}\) and \(\angle ACB = 80^{\circ}\), then \(\angle B=180-(35 + 80)=65^{\circ}\).

Step3: Relate angles and sides

In a triangle, the larger the angle, the longer the side opposite it. Since \(\angle ACB(80^{\circ})>\angle B(65^{\circ})>\angle A(35^{\circ})\), the side opposite \(\angle ACB\) is \(AB\).

Answer:

\(AB\)