Question

Complete.

Each angle of an equiangular triangle has measure

Short answer

Each angle of an equiangular triangle has measure $\mathbf{60}\mathbf{°}$.

Step-by-step solution

Step 1. Description of step.

An equiangular triangle is a triangle in which all the angles of the triangle are equal.

Step 2. Description of step.

Consider a triangle $\Delta ABC$which is equiangular.

As, the triangle $\Delta ABC$is equiangular, therefore $\angle A=\angle B=\angle C$.

The sum of the angles of a triangle is $180°$.

Therefore, the sum of the angles of a triangle $\Delta ABC$is $180°$.

Therefore, it can be obtained that:

$$\begin{gathered} \begin{array}{c}\angle A+\angle B+\angle C=180°\\ \angle A+\angle A+\angle A=180°\end{array} \\ 3\angle A=180° \\ \angle A=\frac{180°}{3} \\ \angle A=60° \end{gathered}$$

Therefore,$\angle A=\angle B=\angle C=60°$

Therefore, if the triangle is equiangular then the measure of the angles of an equiangular triangle are equal and have measure of$60°$ each.

Step 3. Write the complete statement.

Each angle of an equiangular triangle has measure $60°$.