11.1 Angles in Polygons
Quick Review
 Polygon—any closed figure
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with straight sides that do not
cross one another
Regular Polygon—a polygon
with all congruent sides and
all congruent angles
Vertex—Where two sides of a
polygon meet
Interior angle—angle formed
on the inside of a polygon by
two adjacent sides
Exterior angle—angle formed
on the exterior of a polygon
by a vertex and a line drawn
from the vertex.

Angles in Polygons
 Sum of Interior Angles:
 Sum of Exterior Angles
 (n-2)180° = Sum of Int. <
 The sum of the Ext. <‘s in
 Where “n” is the number
of sides in the polygon.
 (the number of sides will
be the same as the
number of angles)
any polygon is 360°.
Example:
 Find the sum of the
interior angles in a
convex Hexagon.
 Hexagon is 6-sided.
 (6-2)180 ° = 720°
 How many sides does a
polygon have if each
exterior angle measures
45 °?
 360/45 = 8
 This is an 8-sided
polygon, aka Octagon.
Find the measure of x
 How many sides?
6
 Sum of Interior Angles?
 (6-2)180 ° = 720 °
 The sum of the given
angles:
 120 +90+110+130+160=610
 720 ° -610 ° = 110 °
 x = 110 °
Find the value of x and the
measure of each angle.
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 How many sides?
5
 Sum of Angles:?
 (5-2)180 = 540
 25x + 40 = 540
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25x = 500
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x = 20
 102° , 65°, 168°, 95°, 110°
Find the value of each interior
angle in each Regular Polygon…
 A Nonagon.
 A 15-gon
 9-sides
 15 sides
 (9-2)180° = 1260°
 (15-2)180° = 2340°
 1260°/9 = 140°
 2340°/15 = 156°
 There are 140° in each
 There are 156° in each
interior angle of a
Nonagon.
interior angle of a 15-gon.
Finding the Number of sides
 If you are given one interior angle of a regular polygon,
you can use that info to find the number of sides.
 Int. Angle = 160°
 Ext. Angle = 180 ° - 160 ° = 20 °
 360 ° /20 ° = 18
 There are 18 sides in this polygon.
Your Turn:
 Find the sum of the
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measures of all interior
angles of the following:
Decagon—
1440°
Heptagon—
900°
Dodecagon—
1800°
 Find the measure of
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each interior angle in a
Regular –
Decagon—
144°
Heptagon—
≈ 128.6
Dodecagon—
150°
Your Turn, Exterior Angles:
 Find the Sum of the
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Exterior Angles in a:
Decagon
360°
Heptagon
360°
Dodecagon
360°
 Find the measure of
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each Exterior Angle of a
Regular …
Decagon
36°
Heptagon
≈ 51.4°
Dodecagon
30°
Your turn again.
 How many sides does a
polygon have if each
interior angle has…
 How many sides does a
 165.6°
 25 sides
regular polygon have if
each exterior angle has a
measure of…
 20°
 18 sides
 162°
 20 sides
 40°
 9 sides
 120°
 6 sides
 15°
 24 sides
Homework
Vocab: Know the names and
number of sides of all the polygons
from triangle to dodecagon (except
the 11-gon)
Pg. 665-668 #6-25 All; 49-54 All;
58-61 All