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.

Practice
Solutions

1.

The art piece is made up of triangles. Triangles can be combined to form different types of polygons. The polygon outlined in the art piece is a hexagon, since it has six sides.

Take a moment to find several different types of polygons in the art piece.

Answer the following questions for the polygons identified in the art piece

a.

Identify each triangle below by side lengths (scalene, isosceles, equilateral) and angle measures (acute, right, obtuse).

Figure a

Figure b

Figure c

b.

Name each of the following polygons that are found in the art piece.

Figure d

Figure e

Figure f

Figure g

Figure h

c.

Find

∠ N

in the polygon below.

d.

Find

∠ T

and

∠ S

in the outlined polygon.

e.

Find

∠ X

in the outlined triangle.

1a.

Identify each triangle below by side lengths (scalene, isosceles, equilateral) and angle measures (acute, right, obtuse).

i. Figure a

ii. Figure b

iii. Figure c

i.

isosceles; obtuse

ii.

scalene; right

iii.

equilateral; acute

1b.

Name each of the following polygons that are found in the art piece.

i. Figure d

ii. Figure e

iii. Figure f

iv. Figure g

v. Figure h

i.

kite

ii.

isosceles trapezoid

iii.

pentagon

iv.

rhombus

v.

heptagon

1c.

Find

∠ N

in the polygon below.

A pentagon has five sides and five angles. Since four angles are given, the missing angle,

∠ N

, can be determined if the sum of angles in a pentagon is known.

The sum of the angles in a pentagon where n = 5 would be:

\begin{array}{rcl} S & = & 180 ° (n - 2) \\ = & 180 ° (5 - 2) \\ = & 180 ° (3) \\ = & 540 ° \end{array}

Substitute the known angles into the formula below and solve for

∠ N

.

\begin{array}{rcl} ∠ A + ∠ B + ∠ C + ∠ D + ∠ E & = & 540 ° \\ 95 ° + 125 ° + 100 ° + 90 ° + ∠ N & = & 540 ° \\ ∠ N + 410 ° & = & 540 ° \\ ∠ N & = & 130 ° \end{array}

1d.

Find

∠ S

and

∠ T

in the outlined polygon.

Quadrilateral QRST is a kite.

Step 1: Find

∠ T

.

∠ R = ∠ T

. Since the angles are located where the two pairs of adjacent sides meet, they are equal. Therefore,

∠ T = 90 °

.

Step 2: Find

∠ S

.

\begin{array}{rcl} ∠ Q + ∠ R + ∠ S + ∠ T & = & 360 ° \\ 65 ° + 90 ° + ∠ S + 90 ° & = & 360 ° \\ ∠ S + 245 ° & = & 360 ° \\ ∠ S & = & 115 ° \end{array}

1e.

Find

∠ X

in the outlined triangle.

∠ Y

is a right angle, which is equal to 90°.

\begin{array}{rcl} ∠ X + ∠ Y + ∠ Z & = & 180 ° \\ ∠ X + 90 ° + 65 ° & = & 180 ° \\ ∠ X + 155 ° & = & 180 ° \\ ∠ X & = & 25 ° \end{array}