HONOR GEOMETRY PRACTICE IN POLYGONS

Problem 1 :

The measure of one exterior angle of a regular polygon is given. Find the number of sides for each.

a) 72°     b) 40°

Solution

Problem 2 :

Find the measure of an interior and an exterior angle of a regular 46-gon.

Solution

Problem 3 :

The measure of one interior angle of a regular polygon is 144°. How many sides does it have?

Solution

Problem 4 :

Five angles of a hexagon have measures 100°, 110°, 120°, 130°, and 140°. What is the measure of the sixth angle?

Solution

Problem 5 :

Find the value of x.

a)

b)

Problem 6 :

The sum of the interior angles of a polygon is 1620°. How many sides does it have?

Solution

Problem 7 :

The measure of the interior angle of a regular polygon is 179°. How many sides does it have?

Solution

Problem 8 :

Find the value of x in the figure given.

Problem 9 :

Find the SUM of the interior angles of each polygon.

a. octagon _____

b. pentagon _____

c. hexagon _____

d. heptagon _____

Solution

Problem 10 :

Find the SUM of the exterior angles of each polygon.

a. octagon _____

b. pentagon _____

Solution

Problem 11 :

What is the measure of EACH interior angle of a regular:

a. octagon _____

b. pentagon _____

c. hexagon _____

d. decagon _____

Solution

Problem 12 :

What is the measure of EACH exterior angle of a regular:

a. octagon _____

b. pentagon _____

c. hexagon _____ 

d. decagon _____

Solution

Problem 13 :

Matching:

Solution

Problem 14 :

Find the value for each variable.

a)

b)

Solution

Problem 15 :

Find each unknown angle measure.

a)

b)

Solution

Problem 16 :

Find the measure of ∠1 in each figure.

a)

b)

Solution

Problem 17 :

Given,

a) How many different ways can the polygon be named?

b) Name a pair of consecutive sides.

c) Name a pair of nonconsecutive vertices.

Solution

Problem 18 :

Find the sum of the interior angles of each convex polygon.

a) nonagon

b) 50-gon

Solution

Problem 19 :

a) Find the measure of each interior angle of a regular hexagon.

b) Find the measure of each exterior angle of a regular decagon.

Solution

Problem 20 :

The measure of each exterior angle in a regular polygon is 24°. How many sides does the polygon have?

Solution