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Chapter 3: Q3 (page 110)

Complete.

Each angle of an equiangular triangle has measure

Short Answer

Expert verified

Each angle of an equiangular triangle has measure 60°.

Step by step solution

01

Step 1. Description of step.

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

02

Step 2. Description of step.

Consider a triangle ΔABCwhich is equiangular.

As, the triangle ΔABCis equiangular, therefore ∠A=∠B=∠C.

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

Therefore, the sum of the angles of a triangle ΔABCis 180°.

Therefore, it can be obtained that:

∠A+∠B+∠C=180°∠A+∠A+∠A=180°3∠A=180°∠A=180°3∠A=60°

Therefore,∠A=∠B=∠C=60°

Therefore, if the triangle is equiangular then the measure of the angles of an equiangular triangle are equal and have measure of60° each.

03

Step 3. Write the complete statement.

Each angle of an equiangular triangle has measure 60°.

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