AnswersSTPSB_Geometry 2627 TreigleAngle Measures of Polygons

Angle Measures of Polygons Answers

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Three interior angles of a quadrilateral measure 55°, 117°, and 120°. What is the measure of the fourth interior angle?

A
68°
B
78°
C
88°
D
98°
2
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Which polygon has an interior angle sum of 1080°?

A
A polygon has 8 sides.
Option A
B
A polygon has 10 sides.
Option B
C
A polygon has 9 sides.
Option C
D
A polygon has 7 sides.
Option D
3

Polygon A B C D E has 5 sides.

Question illustration
A
It is a concave pentagon because segment AE would extend into the inside of the polygon, and it has five sides.
B
It is a convex hexagon because it has six sides and none of the sides would extend into the inside of the polygon.
C
It is a concave hexagon because segment AE would extend into the inside of the polygon, and it has six sides.
D
It is a convex pentagon because it has five sides and none of the sides would extend into the inside of the polygon.
4

A polygon with 7 sides is shown. An angle goes inside of the shape.

Question illustration
A
convex heptagon
B
concave heptagon
C
concave octagon
D
convex octagon
5

A polygon with 5 sides is shown with its exterior angles. The exterior angles are 62 degrees, 66 degrees, 77 degrees, 59 degrees, and (12 x) degrees.

Question illustration
A
6
B
8
C
10
D
12
6

What is the measure of each interior angle of a regular octagon?

A
45º
B
60º
C
120º
D
135º
7

Which statements are true about the regular polygon? Select three options.

A
The sum of the measures of the interior angles is 900°.
B
Each interior angle measures 108°.
C
All of the angles are congruent.
D
The polygon is a regular hexagon.
E
The sum of the measures of the interior angles is 180(5 – 2)°.
8

A polygon with 4 sides is shown with its exterior angles. The exterior angles are 140 degrees, 34 degrees, 56 degrees, and x degrees.

Question illustration
A
100°
B
120°
C
130°
D
150°
9

What is the sum of the measures of the interior angles of a 12-gon?

A
1620°
B
1800°
C
1980°
D
2160°
10

Each exterior angle of a regular decagon has a measure of (3x + 6)°. What is the value of x?

A
x = 8
B
x = 10
C
x = 13
D
x = 18
11

Polygon A B C D E F has 6 sides. Exterior angle A is 62 degrees, exterior angle B is 44 degrees, exterior angle C is 70 degrees, exterior angle D is 60 degrees, and exterior angle E is 43 degrees.

Question illustration
A
79°
B
81°
C
91°
D
99°
12

A polygon with 6 sides is shown. No angles go inside of the shape.

Question illustration
A
convex heptagon
B
concave heptagon
C
concave hexagon
D
convex hexagon
13

Which statements are true about polygons? Select three options.

A
All sides and all angles in a polygon are congruent.
B
The sides of a polygon are segments that intersect exactly two other segments, one at each endpoint.
C
In a polygon, all segments with a common endpoint are collinear.
D
If all of the sides of a convex polygon are extended, none of them will contain any points that are inside the polygon.
E
The extension of at least one side or diagonal in a concave polygon will contain a point that is inside the polygon.
14

An interior angle of a regular polygon has a measure of 135°. What type of polygon is it?

A
hexagon
B
octagon
C
nonagon
D
decagon

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