Properties of Polygons Practice Questions

Review the following concept if necessary: Properties of Polygons Study Guide

Properties of Polygons Practice Questions

Problems

Classify each figure as a convex polygon, a concave polygon, or not a polygon.

Classify each polygon by the number of sides, and determine if each is correctly named.

Which of the following are acceptable names for each polygon?

16. DGFE
17. FDGE
18. EFGD
19. UPQRST
20. RQSPUT
21. UTSPQR
22. What type of polygon is Figure 1? Is it convex or concave?
23. What type of polygon is Figure 2? Is it convex or concave?

Find the sum of the interior angles for each figure.

26. Complete the table for convex polygons.



27. The home plate used in baseball and softball has this shape:



As you can see, there are three right angles and two congruent obtuse angles. What are the measures of the two obtuse angles?

28. Find the measure of an interior angle of a regular octagon.
29. Find the measure of an interior angle of a regular decagon.
30. Find the measure of an exterior angle of a regular hexagon. (Hint: Recall the sum of the exterior angles of a convex polygon.)

Answers

1. not a polygon
2. convex polygon
3. concave polygon
4. convex polygon
5. not a polygon
6. convex polygon
7. concave polygon
8. not a polygon
9. not a polygon
10. quadrilateral, yes
11. triangle, yes
12. pentagon, no
13. heptagon, no
14. hexagon, no
15. octagon, yes
16. yes
17. no
18. yes
19. quadrilateral, convex
20. yes
21. no
22. no
23. hexagon, concave
24. 540°
25. 900°
26. 
27. Home plate is a pentagon, so use the formula with n = 5.

S = 180(n – 2)

S = 180(5 – 2)

S = 180(3)

S = 540

3(right angles) + 2(obtuse angles) = 540

3(90) + 2(obtuse angles) = 540

270 + 2(obtuse angles) = 540

Subtract the 3 right angles to see how much of the original 540 is left.

2(obtuse angles) = 540 – 270 = 270

obtuse angle = 135 (divide by 2 because the two angles share the 270 evenly)

Therefore, each obtuse angle equals 135°. You can check to see that your answer is correct:

90 + 90 + 90 + 135 + 135 = 540.

28. 
29. 
30. x = = 60° (The sum of the exterior angles of a convex polygon is 360°.)