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Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

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Section
BuyFindarrow_forward

Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

In Exercises 45 to 47, write a formal proof for each corollary.

The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles.

To determine

To prove:

The measure of an exterior angle of a triangle equals the sum of the measures of the two nonadjacent interior angles or not.

Explanation

Approach:

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

Calculation:

Consider the triangle as ΔABC with interior angles as m1, m2, m3 and exterior angle at point C as m4.

Figure (1)

Calculate the angles of the right triangle.

m1+m2+m3=180°……(1)

Since, the sum of measures of two supplementary angles is 180°.

m3+m4=180°……(2)

Substitute equation (2) in the equation (1).

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