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Chapter 3: Q27. (page 105)

The formulaS=n-2180 can apply to nonconvex polygons if you allow the measure of an interior angle to be more than 180.

a. Illustrate this with a diagram that shows interior angles with measures greater than 180.

b. Does the reasoning leading up to theorem 3-13 apply to your figure?

Short Answer

Expert verified

a. The diagram that shows interior angles with measures greater than 180 is:

b. Yes, the reasoning leading up to theorem 3-13 apply to figure.

Step by step solution

01

Part a. Step 1. Definition of convex polygon.

A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon..

02

Part a. Step 2. Write the theorem 3-13.

The theorem 3-13 states that the sum of the measures of the angles of a convex polygon withn sides is n-2180.

03

Part a. Step 3. Description of step.

The diagram that shows interior angles with measures greater than 180 is:

04

Part b. Step 1. Definition of convex polygon.

A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon..

05

Part b. Step 2. Write the theorem 3-13.

The theorem 3-13 states that the sum of the measures of the angles of a convex polygon withn sides is n-2180.

06

Part b. Step 3. Description of step.

Yes, the reasoning leading up to theorem 3-13 apply to figure.

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