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Regents Exam Questions Name: ________________________
G.CO.C.11: Interior and Exterior Angles of Polygons 2a
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G.CO.C.11: Interior and Exterior Angles of Polygons 2a
1 Which type of figure is shown in the accompanying diagram?
- hexagon
- octagon
- pentagon
- quadrilateral
2 What is the measure of each interior angle of a regular hexagon?
- 60 °
- 120 °
- 135 °
- 270 °
3 Determine, in degrees, the measure of each interior angle of a regular octagon.
4 Determine and state the measure, in degrees, of an interior angle of a regular decagon.
5 In the diagram below of regular pentagon ABCDE, EB is drawn.
What is the measure of ∠ AEB?
- 36º
- 54º
- 72º
- 108º
6 What is the measure, in degrees, of each exterior angle of a regular hexagon?
- 45
- 60
- 120
- 135
7 A stop sign in the shape of a regular octagon is resting on a brick wall, as shown in the accompanying diagram.
What is the measure of angle x?
- 45°
- 60°
- 120°
- 135°
Regents Exam Questions Name: ________________________
G.CO.C.11: Interior and Exterior Angles of Polygons 2a
www.jmap.org
8 One piece of the birdhouse that Natalie is building is shaped like a regular pentagon, as shown in the accompanying diagram.
If side AE is extended to point F , what is the measure of exterior angle DEF?
- 36°
- 72°
- 108°
- 144°
9 What is the difference between the sum of the measures of the interior angles of a regular pentagon and the sum of the measures of the exterior angles of a regular pentagon?
- 36
- 72
- 108
- 180
10 Find, in degrees, the measures of both an interior angle and an exterior angle of a regular pentagon.
11 The sum of the interior angles of a regular polygon is 720°. How many sides does the polygon have?
- 8
- 6
- 5
- 4
12 The measure of an interior angle of a regular polygon is 120°. How many sides does the polygon have?
- 5
- 6
- 3
- 4
13 Melissa is walking around the outside of a building that is in the shape of a regular polygon. She determines that the measure of one exterior angle of the building is 60°. How many sides does the building have?
- 6
- 9
- 3
- 12
14 A regular polygon has an exterior angle that measures 45°. How many sides does the polygon have?
- 10
- 8
- 6
- 4
15 A regular polygon with an exterior angle of 40° is a
- pentagon
- hexagon
- nonagon
- decagon
16 What is the measure of the largest exterior angle that any regular polygon can have?
- 60º
- 90º
- 120º
- 360º
17 The sum of the interior angles of a regular polygon is 540°. Determine and state the number of degrees in one interior angle of the polygon.
ID: A
G.CO.C.11: Interior and Exterior Angles of Polygons 2a
Answer Section
1 ANS: 1 REF: 060802a 2 ANS: 2
( n − 2)180 = (6 − 2)180 = 720.
REF: 081125ge 3 ANS:
( n − 2)180 = (8 − 2)180 = 1080.
8 =^135.
REF: 061330ge 4 ANS: ( n − 2) n =^
10 =^144
REF: 011531ge 5 ANS: 1
∠ A =
( n − 2) n =^
5 =^108 ∠ AEB^ =^
2 =^36
REF: 081022ge 6 ANS: 2
( n − 2)180 = (6 − 2)180 = 720.
REF: 060213a 7 ANS: 1
( n − 2)180 = (8 − 2)180 = 1080.
8 =^135.^180 −^45 =^135.
REF: 080507a 8 ANS: 2
( n − 2)180 = (5 − 2)180 = 540.
REF: 060718a 9 ANS: 4
( n − 2)180 − n
( n − 2) n
= 180 n − 360 − 180 n + 180 n − 360 = 180 n − 720
REF: 081322ge
ID: A
10 ANS:
= 108 interior. 180 − 108 = 72 exterior
REF: 011131ge 11 ANS: 2 180( n − 2) = 720
n − 2 = 4 n = 6
REF: 061521ge
12 ANS: 2 ( n − 2) n
180 n − 360 = 120 n 60 n = 360 n = 6
REF: 011326ge 13 ANS: 1
Find an interior angle. 180 − x = 60 x = 120
. Find n.
( n − 2) n =^120 180 n − 360 = 120 n 60 n = 360
n = 6
REF: 060423a 14 ANS: 2
180 −
( n − 2) n
180 n − 180 n + 360 = 45 n
360 = 45 n n = 8
REF: 061413ge
ID: A
23 ANS: 3
180( n − 2) = n 180 −
180( n − 2) n
180 n − 360 = 180 n − 180 n + 360
180 n = 720 n = 4
REF: 081223ge
24 ANS: 3
. The sum of the interior angles of a pentagon is (5 − 2)180 = 540.
REF: 011023ge 25 ANS: 1
REF: 080820a 26 ANS: 2 ( n − 2)180 = 1440
n − 2 = 8 n = 10
REF: 011618ge
