   Chapter 2.1, Problem 16E 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

Given: l ∥ m Transversal t m ∠ 1 = 4 x + 2 m ∠ 6 = 4 x − 2 Find: x and m ∠ 5 Exercise 15, 16

To determine

To find:

The value of x and the measure of the given angle.

Explanation

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

Definition:

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

Given:

The given figure is,

lm cut by a transversal t.

The m1=4x+2 and m6=4x2.

Calculation:

Consider the given figure,

From the figure, lm with transversal t.

1 and 6 are exterior angles on the same side of transversal.

m1+m6=180°4x+2+4x2=180°8x=180°x=452

The value of x is 452.

Consider,

m1=4x+2…... (1)

Substitute 452 for x in equation (1)

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