Chapter 12.1, Problem 30E

To determine

To find:Whether a triangle exits or not when two of the angles are supplementary.

Answer to Problem 30E

When two of the angles are supplementary, then no triangle exits.

Explanation of Solution

Given information: Two of the angles are supplementary.

Supplementary angles are those whose sum of the angles is ${180}^{\circ }$ . That is $m\angle 1+m\angle 2={180}^{\circ }$ .

Also, the sum of the angles of a triangle is ${180}^{\circ }$ .

Hence, it is not possible for a triangle to have supplementary angles.

Thus, when two of the angles are supplementary, then no triangle exits.