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Chapter 3: Q6 (page 96)

Explain how each corollary of Theorem 3-11 follows from the theorem

Corollary 2

Short Answer

Expert verified

For an equiangular triangle, measure of each angle must be 60 degrees such that,

60掳+60掳+60掳=180掳

Step by step solution

01

Step 1. State Theorem 3-11

The sum of the angles is1800

02

Step 2. State Corollary 2

Each angle of an equiangular triangle has measure 60.

03

Step 3. State the relation between Theorem 3-11 and Corollary 2.

Since, in an equiangular triangle, all of the angle measures are the same. So, if the three angles of a triangle are each less than 60掳,

Their sum will be less than 1800.

But by theorem 3-11, it is clear that the sum of the three angles of triangle is role="math" localid="1637927723316" 180掳.

So, for equiangular triangle, measure of each angle must be 60 such that.,

60掳+60掳+60掳=180掳.

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