   Chapter 2.CR, Problem 5CR 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: m ∠ D C A = 130 ° m ∠ B A C = 2 x + y m ∠ B C E = 150 ° m ∠ D E C = 2 x − y Find: x and y To determine

To find:

The values of x and y.

Explanation

Given:

The given statement is,

mDCA=130°mBAC=2x+ymBCE=150°mDEC=2xy

And,

AB¯CD¯ and BC¯DE¯.

Figure (1)

Property:

(1) If two parallel lines are cut by a transversal, then a pair of alternate interior angles is congruent.

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

(3) Angles on a straight line add up to 180°.

Calculation:

The given statement is,

mDCA=130°mBAC=2x+ymBCE=150°mDEC=2xy

And,

AB¯CD¯ and BC¯DE¯.

mDCA+mBCE+mBCD=180°

Substitute 130° for mDCA and 150° for mBCE in the above equation.

130°+150°mBCD=180°mBCD=130°+150180°mBCD=100°

B and BCD are alternate interior angles.

BBCDmB=mBCD

Substitute 100° for mBCD in the above equation

mB=100°

BCD and D are alternate interior angles.

BCDDmBCD=mD

Substitute 100° for mBCD in the above equation

mD=100°

BCE is an exterior angle of triangle ΔABC

Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

34. Find the mean of the probability distribution if the probability density function is

Mathematical Applications for the Management, Life, and Social Sciences

Domain Find the domain of the expression. 7. 4x2 10x + 3

Precalculus: Mathematics for Calculus (Standalone Book)

Change each percent to a decimal: 15%

Elementary Technical Mathematics

Place the following set of n = 20 scores in a frequency distribution table.

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Sketch the graphs of the equations in Exercises 512. x+y=1

Finite Mathematics and Applied Calculus (MindTap Course List)

True or False: The function graphed at the right is one-to-one.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th 