Answer The value of x is 8 ° and the value of y is 1 2 ° Explanation Given information :The diagram below Concept Involved: Set up an equation based on the fact that: Alternate interior angles are congruent Triangle Sum Theorem states that Sum of interior angles of triangle adds up to 180 degrees Solve the system of equation using the elimination metho Calculation: Set up an equation based on the fact that alternate interior angles are congruent 2 x + y = 5 x − y Get all the terms in one side of the equation by subtracting 2x and y on both sides 2 x + y - 2 x - y = 5 x - 2 x - y − y Combine like terms on both sides of the equation and label it as 1 s t equation 3 x − 2 y = 0 ➧1 s t equation Use the Triangle Sum theorem which states that sum of interior angle of triangle add up to give 180 degrees to set up the 2 n d equation 5 x + y + 2 x + y + 100 = 180 Group like terms in left side of the equation 5 x + 2 x + y + y + 100 = 180 Combine like terms in left side of the equation 7 x + 2 y + 100 = 180 Subtract 100 on both sides 7 x + 2 y + 100 - 1 0 0 = 180 - 1 0 0 Combine like terms in both sides of the equation and label it as 2 n d equation 7 x + 2 y = 80 ➧2 n d equation Add 1 s t and 2 n d equation to eliminate the variable y 3 x − 2 y = 0 7 x + 2 y = 80 _ 10 x = 80 Divide by 10 on both sides of the equation 10 x 1 0 = 80 1 0 Simplify fraction on both sides of the equation x = 8 Substitute 8 for x in 1 s t equation 3 ( 8 ) − 2 y = 0 Simplify the left side of the equation 24 − 2 y = 0 Subtract 24 on both sides of the equation 24 − 2 y - 2 4 = 0 - 2 4 Combine like terms in both sides of the equation − 2 y = − 24 Divide by -2 on both sides − 2 y - 2 = − 24 - 2 Simplify fraction on both sides of the equation y = 12 Conclusion: The value of x is 8 ° and the value of y is 1 2 °

McDougal Littell Jurgensen Geometry: Student Edition Geometry

5th Edition

ISBN: 9780395977279

Author: Ray C. Jurgensen, Richard G. Brown, John W. Jurgensen

Publisher: Houghton Mifflin Company College Division

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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 3.4, Problem 30WE

To determine

To find:the value of x and y

Expert Solution & Answer

Answer to Problem 30WE

The value of x is 8° and the value of y is 12°

Explanation of Solution

Given information:The diagram below

McDougal Littell Jurgensen Geometry: Student Edition Geometry, Chapter 3.4, Problem 30WE

Concept Involved:

Set up an equation based on the fact that:

Alternate interior angles are congruent
Triangle Sum Theorem states that Sum of interior angles of triangle adds up to 180 degrees

Solve the system of equation using the elimination metho

Calculation: Set up an equation based on the fact that alternate interior angles are congruent

2x+y=5x−y

Get all the terms in one side of the equation by subtracting 2x and y on both sides

2x+y-2x-y=5x-2x-y−y

Combine like terms on both sides of the equation and label it as 1^s^t equation

3x−2y=0

➧1^s^t equation

Use the Triangle Sum theorem which states that sum of interior angle of triangle add up to give 180 degrees to set up the 2ⁿ^d equation

5x+y+2x+y+100=180

Group like terms in left side of the equation

5x+2x+y+y+100=180

Combine like terms in left side of the equation

7x+2y+100=180

Subtract 100 on both sides

7x+2y+100-100=180-100

Combine like terms in both sides of the equation and label it as 2ⁿ^d equation

7x+2y=80

➧2ⁿ^d equation

Add 1^s^t and 2ⁿ^d equation to eliminate the variable y3x−2y=07x+2y=80_10x=80

Divide by 10 on both sides of the equation10x10=8010

Simplify fraction on both sides of the equation

x=8

Substitute 8 for x in 1^s^t equation

3(8)−2y=0

Simplify the left side of the equation

24−2y=0

Subtract 24 on both sides of the equation

24−2y-24=0-24

Combine like terms in both sides of the equation

−2y=−24

Divide by -2 on both sides

−2y-2=−24-2

Simplify fraction on both sides of the equation

y=12

Conclusion:

The value of x is 8° and the value of y is 12°

Chapter 3.4, Problem 29WE

Chapter 3.4, Problem 31WE

Chapter 3 Solutions

McDougal Littell Jurgensen Geometry: Student Edition Geometry

Ch. 3.1 - Prob. 1CE Ch. 3.1 - Prob. 2CE Ch. 3.1 - Prob. 3CE Ch. 3.1 - Prob. 4CE Ch. 3.1 - Prob. 5CE Ch. 3.1 - Prob. 6CE Ch. 3.1 - Prob. 7CE Ch. 3.1 - Prob. 8CE Ch. 3.1 - Prob. 9CE Ch. 3.1 - Prob. 10CE

Ch. 3.1 - Prob. 11CE Ch. 3.1 - Prob. 12CE Ch. 3.1 - Prob. 13CE Ch. 3.1 - Prob. 14CE Ch. 3.1 - Prob. 15CE Ch. 3.1 - Prob. 16CE Ch. 3.1 - Prob. 17CE Ch. 3.1 - Prob. 18CE Ch. 3.1 - Prob. 19CE Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 5WE Ch. 3.1 - Prob. 6WE Ch. 3.1 - Prob. 7WE Ch. 3.1 - Prob. 8WE Ch. 3.1 - Prob. 9WE Ch. 3.1 - Prob. 10WE Ch. 3.1 - Prob. 11WE Ch. 3.1 - Prob. 12WE Ch. 3.1 - Prob. 13WE Ch. 3.1 - Prob. 14WE Ch. 3.1 - Prob. 15WE Ch. 3.1 - Prob. 16WE Ch. 3.1 - Prob. 17WE Ch. 3.1 - Prob. 18WE Ch. 3.1 - Prob. 19WE Ch. 3.1 - Prob. 20WE Ch. 3.1 - Prob. 21WE Ch. 3.1 - Prob. 22WE Ch. 3.1 - Prob. 23WE Ch. 3.1 - Prob. 24WE Ch. 3.1 - Prob. 25WE Ch. 3.1 - Prob. 26WE Ch. 3.1 - Prob. 27WE Ch. 3.1 - Prob. 28WE Ch. 3.1 - Prob. 29WE Ch. 3.1 - Prob. 30WE Ch. 3.1 - Prob. 31WE Ch. 3.1 - Prob. 32WE Ch. 3.1 - Prob. 33WE Ch. 3.1 - Prob. 34WE Ch. 3.1 - Prob. 35WE Ch. 3.1 - Prob. 36WE Ch. 3.1 - Prob. 37WE Ch. 3.1 - Prob. 38WE Ch. 3.1 - Prob. 39WE Ch. 3.1 - 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