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High School Math Algebra High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

Tocalculate: The measure of each labeled angle. The given figure of regular five-pointed star is shown below: The measure of angles are x = 36 ° , y = 72 ° and z = 108 ° . Given information: The given figure is shown below: Formula used: The angle sum property of triangle is: The sum of all angles in a triangle is 180 ° . Each exterior angle in a regular pentagon is equal to 360 ° 5 = 72 ° . Calculation: Consider the given figure. The upper part of the five-pointed star is in triangle form. Since the sum of all angles of the triangle is 180 ° . Thus, x + y + y = 180 ° x + 2 y = 180 ° Each exterior angle in a regular pentagon is equal to 360 ° 5 = 72 ° . Thus, y = 72 ° Also, y + z = 180 ° Put y = 72 ° into the above equation. z = 180 ° − 72 ° z = 108 ° Put y = 72 ° into the equation x + 2 y = 180 ° . x + 2 ( 72 ° ) = 180 ° x = 180 ° − 144 ° x = 36 °

Tocalculate: The measure of each labeled angle. The given figure of regular five-pointed star is shown below: The measure of angles are x = 36 ° , y = 72 ° and z = 108 ° . Given information: The given figure is shown below: Formula used: The angle sum property of triangle is: The sum of all angles in a triangle is 180 ° . Each exterior angle in a regular pentagon is equal to 360 ° 5 = 72 ° . Calculation: Consider the given figure. The upper part of the five-pointed star is in triangle form. Since the sum of all angles of the triangle is 180 ° . Thus, x + y + y = 180 ° x + 2 y = 180 ° Each exterior angle in a regular pentagon is equal to 360 ° 5 = 72 ° . Thus, y = 72 ° Also, y + z = 180 ° Put y = 72 ° into the above equation. z = 180 ° − 72 ° z = 108 ° Put y = 72 ° into the equation x + 2 y = 180 ° . x + 2 ( 72 ° ) = 180 ° x = 180 ° − 144 ° x = 36 °

Solution Summary: The author explains the formula used to calculate the measure of each labeled angle.

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

15th Edition

ISBN: 9780133281163

Author: Prentice Hall

Publisher: Prentice Hall

See similar textbooks

Expert Solution & Answer

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 3.5, Problem 44PPSE

Solution

Tocalculate:The measure of each labeled angle. The given figure of regular five-pointed star is shown below:

The measure of angles are x=36° , y=72° and z=108° .

Given information:

The given figure is shown below:

Formula used:

The angle sum property of triangle is: The sum of all angles in a triangle is 180° .

Each exterior angle in a regular pentagon is equal to 360°5=72° .

Calculation:

Consider the given figure.

The upper part of the five-pointed star is in triangle form.

Since the sum of all angles of the triangle is 180° .

Thus,

x+y+y=180°x+2y=180°

Each exterior angle in a regular pentagon is equal to 360°5=72° .

Thus, y=72°

Also, y+z=180°

Put y=72° into the above equation.

z=180°−72°z=108°

Put y=72° into the equation x+2y=180° .

x+2(72°)=180°x=180°−144°x=36°

Chapter 3.5, Problem 43PPSE

Chapter 3.5, Problem 45PPSE

Chapter 3 Solutions

High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11

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

Ch. 3.1 - Prob. 11PPSE Ch. 3.1 - Prob. 12PPSE Ch. 3.1 - Prob. 13PPSE Ch. 3.1 - Prob. 14PPSE Ch. 3.1 - Prob. 15PPSE Ch. 3.1 - Prob. 16PPSE Ch. 3.1 - Prob. 17PPSE Ch. 3.1 - Prob. 18PPSE Ch. 3.1 - Prob. 19PPSE Ch. 3.1 - Prob. 20PPSE Ch. 3.1 - Prob. 21PPSE Ch. 3.1 - Prob. 22PPSE Ch. 3.1 - Prob. 23PPSE Ch. 3.1 - Prob. 24PPSE Ch. 3.1 - Prob. 25PPSE Ch. 3.1 - Prob. 26PPSE Ch. 3.1 - Prob. 27PPSE Ch. 3.1 - Prob. 28PPSE Ch. 3.1 - Prob. 29PPSE Ch. 3.1 - Prob. 30PPSE Ch. 3.1 - Prob. 31PPSE Ch. 3.1 - Prob. 32PPSE Ch. 3.1 - Prob. 33PPSE Ch. 3.1 - Prob. 34PPSE Ch. 3.1 - Prob. 35PPSE Ch. 3.1 - Prob. 36PPSE Ch. 3.1 - Prob. 37PPSE Ch. 3.1 - Prob. 38PPSE Ch. 3.1 - Prob. 39PPSE Ch. 3.1 - Prob. 40PPSE Ch. 3.1 - Prob. 41PPSE Ch. 3.1 - Prob. 42PPSE Ch. 3.1 - Prob. 43PPSE Ch. 3.1 - Prob. 44PPSE Ch. 3.1 - Prob. 45PPSE Ch. 3.1 - Prob. 46PPSE Ch. 3.1 - Prob. 47PPSE Ch. 3.1 - Prob. 48PPSE Ch. 3.1 - Prob. 49PPSE Ch. 3.1 - Prob. 50PPSE Ch. 3.1 - Prob. 51PPSE Ch. 3.1 - Prob. 52PPSE Ch. 3.1 - Prob. 53PPSE Ch. 3.1 - Prob. 54PPSE Ch. 3.1 - 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