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Elementary Geometry for College St...

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

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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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In Exercise 23 to 30, determine the value of x so that line l will be parallel to line m .

m ∠ 3 = ( x + 1 ) ( x + 4 )

m ∠ 5 = 16 ( x + 3 ) − ( x 2 − 2 )

Chapter 2.3, Problem 29E, In Exercise 23 to 30, determine the value of x so that line l will be parallel to line m.

To determine

To find:

The value of x for the given statement.

Explanation

Given:

The given statement is,

Line 𝓁 and m are cut by transversal t and are parallel to each other.

m∠3=(x+1)(x+4) and m∠5=16(x+3)−(x2−2).

Figure (1)

Theorem:

(1) If two parallel lines are cut by transversal, then the pairs of interior angles on the same side of the transversal are supplementary.

(2) Supplementary angles add up to 180°.

Calculation:

Line 𝓁 is parallel to line m.

∠3 and ∠5 are alternate interior angles on the same side of the transversal.

So,

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