Unit A: Geometry

Chapter 1: Polygons

Practice

Instructions: Click the Download File button to download a printable PDF of the questions. Answer each of the following practice questions on a separate piece of paper. Step by step solutions are provided under the Solutions tab. You will learn the material more thoroughly if you complete the questions before checking the answers.

Download File

Practice
Solutions

What is the measure of each angle in a 25-sided regular polygon to one decimal?

Complete the table below. Sketch the first four polygons listed in the table. Recall that regular polygons have all the same angle measures as well as the same side lengths.

Regular Polygon	Sketch of Polygon	Number of Sides	Sum of Interior Angles of the Polygon (in degrees) (s)	Angle Measure (in degrees, accurate to one decimal place) (M)
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon

Use polygon properties to answer the following.

How does the interior angle measure change as the number of sides increases?

As the number of sides increase, what is happening to the shape of the polygon?

Question 1

What is the measure of each angle in a 25-sided regular polygon to one decimal?

Solution

\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (25 - 2)}{25} \\ = & \frac{180 (23)}{25} \\ = & 165.6 ° \end{array}

Question 2

Complete the table below. Sketch the first four polygons listed in the table. Recall that regular polygons have all the same angle measures as well as the same side lengths.

Regular Polygon	Sketch of Polygon	Number of Sides	Sum of Interior Angles of the Polygon (in degrees) (S)	Angle Measure (in degrees, accurate to one decimal place) (M)
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon

Solution

Regular Polygon	Number of Sides	Sum of Interior Angles of the Polygon (in degrees) (S)	Angle Measure (in degrees, accurate to one decimal place) (M)
Pentagon	5	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (5 - 2) \\ = & 180 ° (3) \\ = & 540 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (5 - 2)}{5} \\ = & \frac{180 (3)}{5} \\ = & 108 ° \end{array}$
Hexagon	6	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (6 - 2) \\ = & 180 ° (4) \\ = & 720 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (6 - 2)}{6} \\ = & \frac{180 (4)}{6} \\ = & 120 ° \end{array}$
Heptagon	7	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (7 - 2) \\ = & 180 ° (5) \\ = & 900 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (7 - 2)}{7} \\ = & \frac{180 (5)}{7} \\ = & 128.6 ° \end{array}$
Octagon	8	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (8 - 2) \\ = & 180 ° (6) \\ = & 1 080 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (8 - 2)}{8} \\ = & \frac{180 (8)}{6} \\ = & 135 ° \end{array}$
Nonagon	9	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (9 - 2) \\ = & 180 ° (7) \\ = & 1 260 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (9 - 2)}{9} \\ = & \frac{180 (7)}{9} \\ = & 140 ° \end{array}$
Decagon	10	$\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (10 - 2) \\ = & 180 ° (8) \\ = & 1 440 ° \end{array}$	$\begin{array}{rcl} M & = & \frac{180 (n - 2)}{n} \\ = & \frac{180 (10 - 2)}{10} \\ = & \frac{180 (8)}{10} \\ = & 144 ° \end{array}$

Question 3

Use polygon properties to answer the following.

How does the interior angle measure change as the number of sides increases?

As the number of sides increase, what is happening to the shape of the polygon?

Solution

As the number of sides increase, the measure of the interior angle increases.

As the number of sides increase, the polygon looks more like a circle.