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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掳.

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 螖ABCwhich is equiangular.

As, the triangle 螖ABCis equiangular, therefore 鈭�A=鈭�B=鈭�C.

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

Therefore, the sum of the angles of a triangle 螖ABCis 180掳.

Therefore, it can be obtained that:

鈭�A+鈭�B+鈭�C=180掳鈭�A+鈭�A+鈭�A=180掳3鈭�A=180掳鈭�A=180掳3鈭�A=60掳

Therefore,鈭�A=鈭�B=鈭�C=60掳

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

03

Step 3. Write the complete statement.

Each angle of an equiangular triangle has measure 60掳.

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