   Chapter 2.4, Problem 23E Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

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

Consider any triangle and one exterior angle at each vertex. What is the sum of the measures of the measures of the three exterior angle of the triangles?

To determine

To find:

The sum of the measures of three exterior angles of the triangle.

Explanation

Consider the following triangle.

Figure (1)

(1) Sum of three angles in a triangle is equal to 180°.

(2) The measure of an exterior of a triangle is equal to the sum of the measures of two non-adjacent interior angles.

Calculation:

Equate the sum of all three angles of triangle to 180°.

m1+m2+m3=180°

Equate the exterior of a triangle is to the sum of the measures of two non-adjacent interior angles.

m4=+m2+m3(1)

m5=+m1+m3(2)

m6=+m1+m2(3)

Add equation (1), (2), and (3) in order to obtain the sum of exterior angles.

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