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Essential Question: How do you find
interior and exterior angle measures
of polygons?
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Before we
start…
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What is a polygon?
A closed figure whose
line sides are line
segments that intersect
only at their endpoints.
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What is a regular polygon?
A polygon whose sides
are all the same length
and whose angles are
all the same measure
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How are polygons identified?
Polygons are identified by their number of sides.
Number of Sides
Name
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Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
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Heptagon
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Octagon
9
Nonagon
10
Decagon
12
Dodecagon
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What is an interior angle?
An angle inside the
polygon
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How do you find interior angle
measures in a polygon?
Use the formula:
Sum of angle measures in an n-gon:
𝑛 − 2 ∙ 180°
Measure of one angle in a regular n-gon:
𝑛 − 2 ∙ 180°
𝑛
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Find the sum of the angle measures in a 9-gon.
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Find the sum of the angle measures in a octagon.
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Find the sum of the angle measures in a 15-gon.
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Find the sum of the angle measures in a
pentagon.
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Find the sum of the angle measures in a hexagon.
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Find the measure of one angle in a regular
heptagon. Round to the nearest tenth of a degree.
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Find the measure of one angle in a regular 15gon. Round to the nearest tenth of a degree.
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Find the measure of one angle in a regular
octagon. Round to the nearest tenth of a degree.
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Find the measure of one angle in a regular
decagon. Round to the nearest tenth of a degree.
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Find the measure of one angle in a regular 20gon. Round to the nearest tenth of a degree.
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What is an exterior angle?
When you extend a side
of a polygon, the angle
that is adjacent to the
interior angle
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How do you find the measure of an
exterior angle?
The exterior angle and its adjacent interior angle
form a straight angle.
These two angles will add up to 180°
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Find 𝑚∠1 in the diagram.
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Find 𝑚∠1 in the diagram.
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Find 𝑚∠3 in the diagram.
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Find 𝑚∠5 in the diagram.
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Sum of Exterior Angles
The sum of the measures of the exterior angles at
the vertex of a convex polygon is 360°.
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Find the unknown angle measure in the diagram.
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Find the unknown angle measure in the diagram.
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How do you find angle measures in polygons?
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Ticket Out the Door
Find the missing angles.
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