a Answer The sum of the measures of the angles of the nonconvex polygon is 540 ° Explanation Given information: Nonconvex polygon as pentagon The sum of the measures of the angles of the nonconvex polygon of ‘ n’ sides is given by ( n − 2 ) × 180 ° Here in the figure, n = 5 Therefore, The sum of the measures of the angles of the nonconvex polygon will be ( 5 − 2 ) × 180 ° = 540 ° b To determine To demonstrate: The sum of the measures of the angles of the nonconvex octagon is 1080 ° Answer The sum of the measures of the angles of the nonconvex octagon is 1080 ° Explanation Given information: Nonconvex polygon as Octagon The sum of the measures of the angles of the nonconvex polygon is given by ( n − 2 ) × 180 ° Here, n = 8 Therefore, The sum of the measures of the angles of the nonconvex polygon = ( 8 − 2 ) × 180 ° = 6 × 180 ° = 1080 ° c To determine To demonstrate: The sum of the measures of the angles of the nonconvex polygon of sides ‘ n’ is ( n − 2 ) × 180 ° Answer Yes, the sum of the measures of the angles of the nonconvex polygon is ( n − 2 ) × 180 ° Explanation Given information: The sum of the measures of the angles of the nonconvex polygon of ‘n’ sides is ( n − 2 ) × 180 ° Yes, the sum of the measures of the angles of the nonconvex polygon is given by ( n − 2 ) × 180 ° d To determine To demonstrate: The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360 ° Answer The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360 ° Explanation Given information: The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360 ° For any closed structure, formed by sides and vertex, the sum of the exterior angles is always equal to the sum of linear pairs and sum of interior angles. Therefore, N = 180 n – 180 ( n − 2 ) N = 180 n – 180 n + 360 N = 360 Hence, we got the sum of exterior angles of n vertex equal to 360 degrees.

91st Edition

ISBN: 9780866099653

Author: Richard Rhoad, George Milauskas, Robert Whipple

Publisher: McDougal Littell

See similar textbooks

Videos

Question

Chapter 7.3, Problem 22PSC

To determine

To demonstrate: The sum of the measures of the angles of the nonconvex polygon is 540°

Expert Solution

Answer to Problem 22PSC

The sum of the measures of the angles of the nonconvex polygon is 540°

Explanation of Solution

Given information:

Nonconvex polygon as pentagon

The sum of the measures of the angles of the nonconvex polygon of ‘ n’ sides is given by (n−2)×180°

Here in the figure, n = 5

Therefore, The sum of the measures of the angles of the nonconvex polygon will be (5−2)×180°=540°

To determine

To demonstrate: The sum of the measures of the angles of the nonconvex octagon is 1080°

Expert Solution

Answer to Problem 22PSC

The sum of the measures of the angles of the nonconvex octagon is 1080°

Explanation of Solution

Given information:

Nonconvex polygon as Octagon

The sum of the measures of the angles of the nonconvex polygon is given by (n−2)×180°

Here, n = 8

Therefore, The sum of the measures of the angles of the nonconvex polygon = (8−2)×180°=6×180°=1080°

To determine

To demonstrate: The sum of the measures of the angles of the nonconvex polygon of sides ‘ n’ is (n−2)×180°

Expert Solution

Answer to Problem 22PSC

Yes, the sum of the measures of the angles of the nonconvex polygon is (n−2)×180°

Explanation of Solution

Given information:

The sum of the measures of the angles of the nonconvex polygon of ‘n’ sides is (n−2)×180°

Yes, the sum of the measures of the angles of the nonconvex polygon is given by (n−2)×180°

To determine

To demonstrate: The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360°

Expert Solution

Answer to Problem 22PSC

The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360°

Explanation of Solution

Given information:

The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360°

For any closed structure, formed by sides and vertex, the sum of the exterior angles is always equal to the sum of linear pairs and sum of interior angles. Therefore,

N = 180n – 180(n−2)N = 180n – 180n+ 360N = 360

Hence, we got the sum of exterior angles of n vertex equal to 360 degrees.

Chapter 7.3, Problem 21PSC

Chapter 7.3, Problem 23PSC

Chapter 7 Solutions

Geometry For Enjoyment And Challenge

Ch. 7.1 - Prob. 1PSA Ch. 7.1 - Prob. 2PSA Ch. 7.1 - Prob. 3PSA Ch. 7.1 - Prob. 4PSA Ch. 7.1 - Prob. 5PSA Ch. 7.1 - Prob. 6PSA Ch. 7.1 - Prob. 7PSA Ch. 7.1 - Prob. 8PSA Ch. 7.1 - Prob. 9PSA Ch. 7.1 - Prob. 10PSA

Ch. 7.1 - Prob. 11PSA Ch. 7.1 - Prob. 12PSB Ch. 7.1 - Prob. 13PSB Ch. 7.1 - Prob. 14PSB Ch. 7.1 - Prob. 15PSB Ch. 7.1 - Prob. 16PSB Ch. 7.1 - Prob. 17PSB Ch. 7.1 - Prob. 18PSB Ch. 7.1 - Prob. 19PSC Ch. 7.1 - Prob. 20PSC Ch. 7.1 - Prob. 21PSC Ch. 7.1 - Prob. 22PSC Ch. 7.1 - Prob. 23PSC Ch. 7.2 - Prob. 1PSA Ch. 7.2 - Prob. 2PSA Ch. 7.2 - Prob. 3PSA Ch. 7.2 - Prob. 4PSA Ch. 7.2 - Prob. 5PSA Ch. 7.2 - Prob. 6PSA Ch. 7.2 - Prob. 7PSA Ch. 7.2 - Prob. 8PSA Ch. 7.2 - Prob. 9PSA Ch. 7.2 - Prob. 10PSA Ch. 7.2 - Prob. 11PSB Ch. 7.2 - Prob. 12PSB Ch. 7.2 - Prob. 13PSB Ch. 7.2 - Prob. 14PSB Ch. 7.2 - Prob. 15PSB Ch. 7.2 - Prob. 16PSB Ch. 7.2 - Prob. 17PSC Ch. 7.2 - Prob. 18PSC Ch. 7.2 - Prob. 19PSC Ch. 7.2 - Prob. 20PSD Ch. 7.3 - Prob. 1PSA Ch. 7.3 - Prob. 2PSA Ch. 7.3 - Prob. 3PSA Ch. 7.3 - Prob. 4PSA Ch. 7.3 - Prob. 5PSA Ch. 7.3 - Prob. 6PSA Ch. 7.3 - Prob. 7PSA Ch. 7.3 - Prob. 8PSB Ch. 7.3 - Prob. 9PSB Ch. 7.3 - Prob. 10PSB Ch. 7.3 - Prob. 11PSB Ch. 7.3 - Prob. 12PSB Ch. 7.3 - Prob. 13PSB Ch. 7.3 - Prob. 14PSB Ch. 7.3 - Prob. 15PSB Ch. 7.3 - Prob. 16PSB Ch. 7.3 - Prob. 17PSB Ch. 7.3 - Prob. 18PSB Ch. 7.3 - Prob. 19PSB Ch. 7.3 - Prob. 20PSC Ch. 7.3 - Prob. 21PSC Ch. 7.3 - Prob. 22PSC Ch. 7.3 - Prob. 23PSC Ch. 7.3 - Prob. 24PSD Ch. 7.4 - Prob. 1PSA Ch. 7.4 - Prob. 2PSA Ch. 7.4 - Prob. 3PSA Ch. 7.4 - Prob. 4PSA Ch. 7.4 - Prob. 5PSA Ch. 7.4 - Prob. 6PSA Ch. 7.4 - Prob. 7PSA Ch. 7.4 - Prob. 8PSB Ch. 7.4 - Prob. 9PSB Ch. 7.4 - Prob. 10PSB Ch. 7.4 - Prob. 11PSB Ch. 7.4 - Prob. 12PSB Ch. 7.4 - Prob. 13PSB Ch. 7.4 - Prob. 14PSC Ch. 7.4 - Prob. 15PSC Ch. 7.4 - Prob. 16PSC Ch. 7.4 - Prob. 17PSC Ch. 7 - Prob. 1RP Ch. 7 - Prob. 2RP Ch. 7 - Prob. 3RP Ch. 7 - Prob. 4RP Ch. 7 - Prob. 5RP Ch. 7 - Prob. 6RP Ch. 7 - Prob. 7RP Ch. 7 - Prob. 8RP Ch. 7 - Prob. 9RP Ch. 7 - Prob. 10RP Ch. 7 - Prob. 11RP Ch. 7 - Prob. 12RP Ch. 7 - Prob. 13RP Ch. 7 - Prob. 14RP Ch. 7 - Prob. 15RP Ch. 7 - Prob. 16RP Ch. 7 - Prob. 17RP Ch. 7 - Prob. 18RP Ch. 7 - Prob. 19RP Ch. 7 - Prob. 20RP Ch. 7 - Prob. 21RP Ch. 7 - Prob. 22RP Ch. 7 - Prob. 23RP Ch. 7 - Prob. 24RP Ch. 7 - Prob. 25RP Ch. 7 - Prob. 26RP Ch. 7 - Prob. 27RP Ch. 7 - Prob. 28RP Ch. 7 - Prob. 29RP Ch. 7 - Prob. 30RP

Additional Math Textbook Solutions

Find more solutions based on key concepts

Drug for Nausea Ondansetron (Zofran) is a drug used by some pregnant women for nausea. There was some concern t...

Introductory Statistics

In Problems 25-32, the graph of a function is given. Use the graph to find: a. The intercepts, if any b. The do...

Precalculus

Fill in each blank so that the resulting statement is true. The quadratic function f(x)=a(xh)2+k,a0, is in ____...

Algebra and Trigonometry (6th Edition)

A student has to sell 2 books from a collection of 6 math, 7 science, and 4 economics books. How many choices a...

A First Course in Probability (10th Edition)

Constructing Frequency Distributions. In Exercises 11–18, use the indicated data to construct the frequency dis...

Elementary Statistics (13th Edition)

Whether the ‘Physicians Committee for Responsible Medicine’ has the potential to create a bias in a statistical...

Elementary Statistics

Knowledge Booster

$Geometry$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.

To demonstrate: The sum of the measures of the angles of the nonconvex polygon is 540 °

Videos

To demonstrate: The sum of the measures of the angles of the nonconvex polygon is 540°

Answer to Problem 22PSC

Explanation of Solution

To demonstrate: The sum of the measures of the angles of the nonconvex octagon is 1080°

Answer to Problem 22PSC

Explanation of Solution

To demonstrate: The sum of the measures of the angles of the nonconvex polygon of sides ‘ n’ is (n−2)×180°

Answer to Problem 22PSC

Explanation of Solution

To demonstrate: The sum of the measures of the exterior angles of the nonconvex polygon of sides ‘ n’ is 360°

Answer to Problem 22PSC

Explanation of Solution

Chapter 7 Solutions

Additional Math Textbook Solutions