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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Prob. 2ST1 Ch. 3.3 - Prob. 3ST1 Ch. 3.3 - Prob. 4ST1 Ch. 3.3 - Prob. 5ST1 Ch. 3.3 - Prob. 6ST1 Ch. 3.3 - Prob. 7ST1 Ch. 3.3 - Prob. 8ST1 Ch. 3.3 - Prob. 9ST1 Ch. 3.3 - Prob. 10ST1 Ch. 3.3 - Prob. 11ST1 Ch. 3.3 - Prob. 12ST1 Ch. 3.3 - Prob. 13ST1 Ch. 3.3 - Prob. 14ST1 Ch. 3.3 - Prob. 15ST1 Ch. 3.3 - Prob. 16ST1 Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.3 - Prob. 4E Ch. 3.3 - Prob. 5E Ch. 3.3 - Prob. 6E Ch. 3.3 - Prob. 7E Ch. 3.3 - Prob. 8E Ch. 3.4 - Prob. 1CE Ch. 3.4 - Prob. 2CE Ch. 3.4 - Prob. 3CE Ch. 3.4 - Prob. 4CE Ch. 3.4 - Prob. 5CE Ch. 3.4 - Prob. 6CE Ch. 3.4 - Prob. 7CE Ch. 3.4 - Prob. 8CE Ch. 3.4 - Prob. 9CE Ch. 3.4 - Prob. 10CE Ch. 3.4 - Prob. 11CE Ch. 3.4 - Prob. 12CE Ch. 3.4 - Prob. 13CE Ch. 3.4 - Prob. 14CE Ch. 3.4 - Prob. 15CE Ch. 3.4 - Prob. 16CE Ch. 3.4 - Prob. 17CE Ch. 3.4 - Prob. 1WE Ch. 3.4 - Prob. 2WE Ch. 3.4 - Prob. 3WE Ch. 3.4 - Prob. 4WE Ch. 3.4 - Prob. 5WE Ch. 3.4 - Prob. 6WE Ch. 3.4 - Prob. 7WE Ch. 3.4 - Prob. 8WE Ch. 3.4 - Prob. 9WE Ch. 3.4 - 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Prob. 1ST2 Ch. 3.6 - Prob. 2ST2 Ch. 3.6 - Prob. 3ST2 Ch. 3.6 - Prob. 4ST2 Ch. 3.6 - Prob. 5ST2 Ch. 3.6 - Prob. 6ST2 Ch. 3.6 - Prob. 7ST2 Ch. 3.6 - Prob. 8ST2 Ch. 3.6 - Prob. 9ST2 Ch. 3.6 - Prob. 10ST2 Ch. 3.6 - Prob. 11ST2 Ch. 3.6 - Prob. 12ST2 Ch. 3.6 - Prob. 13ST2 Ch. 3.6 - Prob. 14ST2 Ch. 3.6 - Prob. 15ST2 Ch. 3 - Prob. 1CR Ch. 3 - Prob. 2CR Ch. 3 - Prob. 3CR Ch. 3 - Prob. 4CR Ch. 3 - Prob. 5CR Ch. 3 - Prob. 6CR Ch. 3 - Prob. 7CR Ch. 3 - Prob. 8CR Ch. 3 - Prob. 9CR Ch. 3 - Prob. 10CR Ch. 3 - Prob. 11CR Ch. 3 - Prob. 12CR Ch. 3 - Prob. 13CR Ch. 3 - Prob. 14CR Ch. 3 - Prob. 15CR Ch. 3 - Prob. 16CR Ch. 3 - Prob. 17CR Ch. 3 - Prob. 18CR Ch. 3 - Prob. 19CR Ch. 3 - Prob. 20CR Ch. 3 - Prob. 21CR Ch. 3 - Prob. 1CT Ch. 3 - Prob. 2CT Ch. 3 - Prob. 3CT Ch. 3 - Prob. 4CT Ch. 3 - Prob. 5CT Ch. 3 - Prob. 6CT Ch. 3 - Prob. 7CT Ch. 3 - Prob. 8CT Ch. 3 - Prob. 9CT Ch. 3 - Prob. 10CT Ch. 3 - Prob. 11CT Ch. 3 - Prob. 12CT Ch. 3 - Prob. 13CT Ch. 3 - Prob. 14CT Ch. 3 - Prob. 1AR Ch. 3 - Prob. 2AR Ch. 3 - 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