Chapter 5.6, Problem 37PPS

To determine

To find:To investigate the properties of polygons.

Answer to Problem 37PPS

A: Polygons have been drawn.

B: Measurement of the angles have been written.

C: Relationship from Inductive Reasoning.

D: Inductive reasoning.

E: $180(n-2)$

Explanation of Solution

Given:Graph of possible polygons.

  

A: Polygons have been drawn.

b:

Number of sides	Angle Measure				Sum of Angles
3	$m\angle A$	${71.3}^0$	$m\angle B$	${65.3}^0$	${180}^0$
	$m\angle C$	${43.4}^0$
4	$m\angle F$`	${108}^0$	$m\angle G$	${89.3}^0$	${360}^0$
	$m\angle H$	${81}^0$	$m\angle J$	${81}^0$
5	$m\angle P$	${104.6}^0$	$m\angle Q$	${113.5}^0$	${540}^0$
	$m\angle R$	${114.6}^0$	$m\angle S$	${106}^0$
	$m\angle T$	${101.3}^0$

c: As per inductive reasoning , since the sum of angles are all multiples of 180 so by relating this the total number of sides . So now it can be conjectured that the sum of the angles of the polygons is equal to 180 times and 2 less than the total numbers of the sides of polygon.

d: Inductive reasoning was used here.

e: Algebraic expression for the sum of measures of angles for a polygon with $n$ sides is $180(n-2)$ .