   Chapter 2.1, Problem 16E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# Given: m ∥ n Transversal k m ∠ 1 = 5 x + y m ∠ 2 = 3 x + y m ∠ 8 = 3 x + 5 y Find: x , y , and m ∠ 8 Exercise 1 7 - 1 9

To determine

To find:

The values of x, y and the measure of the given angle.

Explanation

If there exists two parallel lines cut by a transversal then the pair of exterior angles on the same side of transversal is supplementary.

The sum of angles that falls on the straight line is 180°.

Given:

The given figure is,

mn cut by a transversal k.

m1=5x+y, m2=3x+y and m8=3x+5y.

The given angle is 8.

Calculation:

Consider the given figure,

From the figure, mn with transversal k.

1 and 2 fall on the straight line m.

m1+m2=1805x+y+3x+y=1808x+2y=1804x+y=90.......(1)

From the figure (1), mn with transversal k.

4 and 6 are the exterior angles on the same side of transversal k

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