Properties of Polygons_ Tutorial3
pdf
keyboard_arrow_up
School
University of South Carolina *
*We aren’t endorsed by this school
Course
A503
Subject
Mathematics
Date
Apr 3, 2024
Type
Pages
6
Uploaded by MegaStar111012
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
1/6
Lesson Activity
Regular Convex Polygons
This activity will help you meet these educational goals:
You will explore regular convex polygons by applying the interior angle sum theorem and the
relationships between interior and exterior angles.
Directions
Read the instructions for this self-checked activity. Type in your response to each question,
and check your answers. At the end of the activity, write a brief evaluation of your work.
Activity
In this activity, you will apply what you've learned about the sum of the interior and exterior
angles of convex polygons and regular convex polygons.
Question 1
The sum of the measures of the interior angles of a convex polygon is . How many sides
does the polygon have?
Answer:
50
Space used (includes formatting): 9 / 15000
Hide Sample Answer
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
2/6
The sum of the interior angles of a convex polygon is
. Therefore,
. Solve for
The polygon has 50 sides.
Question 2
An interior angle of a regular convex polygon is
. How many sides does the polygon have?
Answer:
15 sides
Space used (includes formatting): 15 / 15000
Since the polygon is regular, all interior angles are congruent, and all exterior angles are
congruent. Using the fact that an interior and exterior angle form a linear pair, solve for an
exterior angle:
.
Solve for the number of sides:
.
The polygon has
sides.
Hide Sample Answer
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
3/6
Question 3
Fill in the missing information in the table.
Answer:
Regular Polygon
Interior Angle
Sum
One Interior
Angle
Exterior Angle
Sum
One Exterior
Angle
hexagon
108°
45°
decagon
1800°
90°
Space used (includes formatting): 1096 / 15000
Regular Polygon
Interior Angle Sum
One Interior Angle
Exterior Angle Sum
One Exterior Angle
hexagon
720°
120°
360°
60°
pentagon
540°
108°
360°
72°
octagon
1080°
135°
360°
45°
decagon
1440°
144°
360°
36°
12-gon
1800°
150°
360°
30°
quadrilateral
360°
90°
360°
90°
Hide Sample Answer
Question 4
The expressions in this figure represent the measures of the interior angles. Solve for the
value of x
.
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
4/6
Answer:
31.82
Space used (includes formatting): 12 / 15000
This is a convex polygon with seven sides. Use the formula for the sum of the interior angles:
.
Set this value equal to the sum of the expressions for each angle given in the figure:
Hide Sample Answer
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
5/6
Question 5
Suppose the set designer from the introduction needs to install a brace to support a regular
pentagonal stage structure. He wants the brace to be in line with the side that it’s attached
to. At what angle, represented as in the figure, should he secure the brace to the ground?
Answer:
36 degrees
Space used (includes formatting): 17 / 15000
The sum of the exterior angles of the pentagon is
. Therefore, the two other angles of the
triangle created by the brace and the ground are
. The angles of the triangle must
sum to
.
Hide Sample Answer
2/28/24, 12:18 PM
Lesson Activity: Regular Convex Polygons
https://f1.app.edmentum.com/courseware-delivery/ua/125276/45610409/aHR0cHM6Ly9mMS5hcHAuZWRtZW50dW0uY29tL2x0aS92Mi9sZWFybmV…
6/6
The stage designer should secure the brace to the ground at a
angle.
Self-Evaluation
How did you do? Rate your work on a scale of 1 to 5, with 5 as the highest score. Then write a
brief evaluation of your work below. Note what you learned and what challenged you.
Answer:
4
Space used (includes formatting): 8 / 15000
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help