Question

a triangle has two angles that measure 50° and 60°. which side in the triangle is the longest? ○ all sides are equal. ○ the side opposite the 50° angle. ○ the side opposite the 60° angle. ○ the side opposite the third angle.

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^\circ\). Let the third angle be \(x\). So, \(50^\circ + 60^\circ + x = 180^\circ\). Solving for \(x\), we get \(x = 180^\circ - 50^\circ - 60^\circ = 70^\circ\).

Step2: Relate angle size to side length

In a triangle, the longest side is opposite the largest angle. The angles are \(50^\circ\), \(60^\circ\), and \(70^\circ\). The largest angle is \(70^\circ\) (the third angle), so the side opposite the third angle is the longest.

Answer:

The side opposite the third angle.