Transcript Glencoe Math Connects, Course 3

Main Idea and New Vocabulary
NGSSS
Example 1: Classify Polygons
Key Concept: Interior Angle Sum of a Polygon
Example 2: Sum of Interior Angle Measures
Example 3: Real-World Example
Five-Minute Check
• Find the sum of the angle measures of a
polygon and the measure of an interior angle of
a regular polygon.
• polygon
• interior angle
• equiangular
• regular polygon
MA.8.G.2.3 Demonstrate that the sum of the
angles in a triangle is 180-degrees and
apply this fact to find unknown measure of
angles, and the sum of angles in polygons.
Classify Polygons
Determine whether the figure is a polygon. If it is,
classify the polygon. If it is not a polygon, explain
why.
Answer: It is not a polygon because it has a curved
side.
Determine whether the figure is a
polygon. If it is, classify the
polygon. If it is not a polygon,
explain why.
A. yes; pentagon
B. yes; hexagon
C. yes; heptagon
D. No; the segments do not intersect
at their endpoints.
Sum of Interior Angle Measures
ALGEBRA Find the sum of the measures of the
interior angles of a 13-gon.
S = (n – 2)180
Write an equation.
S = (13 – 2)180
A 13-gon has 13 sides.
Replace n with 13.
S = (11)180 or 1,980
Simplify.
Answer: The sum of the measures of the interior
angles of a 13-gon is 1,980°.
ALGEBRA Find the sum of the measures of the
interior angles of an 18-gon.
A. 160°
B. 2,880°
C. 3,060°
D. 3,240°
DESIGN A designer is creating a new logo for a
bank. The logo consists of a regular pentagon
surrounded by isosceles triangles. Find the
measure of an interior angle of a regular
pentagon.
Step 1 Find the sum of the measures of the angles.
S = (n – 2)180
Write an equation.
S = (5 – 2)180
Replace n with 6.
S = (3)180 or 540
Simplify.
The sum of the measures of the interior angles
is 540°.
Step 2 Divide 540 by 5, the number of interior angles,
to find the measure of one interior angle.
540 ÷ 5 = 108
Answer: The measure of one interior angle of a
regular pentagon is 108°.
ART An artist is creating a sculpture that is
made up of regular decagons. Find the measure
of an interior angle of a regular decagon.
A. 144°
B. 225°
C. 1,440°
D. 1,800°
Find the sum of the measures of the interior
angles of a hexagon.
A. 120°
B. 360°
C. 720°
D. 1,080°
Find the sum of the measures of the interior
angles of a nonagon.
A. 140°
B. 1,080°
C. 1,260°
D. 1,620°
Find the measure of one interior angle in a
regular octagon. Round to the nearest tenth if
necessary.
A. 120°
B. 135°
C. 180°
D. 1,080°
Find the measure of one interior angle in a
regular 14-gon. Round to the nearest tenth if
necessary.
A. 154.3°
B. 180°
C. 2,160°
D. 2,520°
Find the measure of one interior angle in a
regular 56-gon. Round to the nearest tenth if
necessary.
A. 173.6°
B. 176.8°
C. 186.7°
D. 9,720°
The following statements are true about triangle XYZ.
• The measure of each angle is evenly divisible by 20.
• mX is greater than mZ.
• mZ is greater than mY.
• mY + mZ =
mX.
What are the angle measures of triangle XYZ?
A. mX = 120°, mY = 20°, mZ = 40°
B.
mX = 120°, mY = 30°, mZ = 30°
C.
mX = 130°, mY = 20°, mZ = 30°
D.
mX = 110°, mY = 50°, mZ = 20°