Chapter 7.3, Problem 14PSB

a

To determine

“If the number of the sides of a polygon increases, the number of the exterior angles increases” is always, sometimes or never be true.

Answer to Problem 14PSB

Final answer for the statement is A

Explanation of Solution

Given information :

The following statement has been given

“As the number of sides of a polygon increases, the number of exterior angles increase “

We know that as the number of sides increases, the number of interior angles increases. Thus, for every interior angle, one exterior increases.

Thus, this statement is always true

b

To determine

To check, whether the given statement is always, sometimes or never be true.

Answer to Problem 14PSB

Final answer for the statement is N

Explanation of Solution

Given information :

The following statement has been given

As the number of sides of a polygon increases, the sum of the measures of exterior angles increases

We know that the sum of the measure of the exterior angles of any polygon will always remain constant.

Thus, this statement is never true

c

To determine

To check, that the given statement will lies in which of section i.e. A,S and N.

Answer to Problem 14PSB

Final answer for the statement is N

Explanation of Solution

Given information :

The following statement has been given

The sum of the lengths of the diagonals of a polygon is greater than the perimeter of the polygon

We know that the diagonals are nothing but vector addition of the sides of the polygon. Thus, the modulus of an added vector can never be greater than the modulus value of the original vectors

Thus, this statement is never true

d

To determine

To given statement is always true, sometimes true or never be true.

Answer to Problem 14PSB

Final answer for the statement is A

Explanation of Solution

Given information :

The following statement has been given

The sum of the measures of the angles of a polygon formed by joining consecutive midpoints of a polygon’s sides is equal to the sum of the measures of the angles of the original polygon.

We know that the measure of the sum of angles any n sided polygon is always constant. Now, we know that a polygon formed by joining the midpoints of the original one will also have the same number of sides, thus the sum will remain constant.

Thus, this statement is always true