Geometry For Enjoyment And Challenge
Geometry For Enjoyment And Challenge
91st Edition
ISBN: 9780866099653
Author: Richard Rhoad, George Milauskas, Robert Whipple
Publisher: McDougal Littell
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Chapter 7.3, Problem 22PSC

a

To determine

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

a

Expert Solution
Check Mark

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°

b

To determine

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

b

Expert Solution
Check Mark

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°

c

To determine

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

c

Expert Solution
Check Mark

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°

d

To determine

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

d

Expert Solution
Check Mark

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.

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Chapter 7.3, Problem 21PSC
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Chapter 7.3, Problem 23PSC

Chapter 7 Solutions

Geometry For Enjoyment And Challenge

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

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