Find Angle Measures in Polygons
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Transcript Find Angle Measures in Polygons
FIND ANGLE MEASURES IN
POLYGONS
Ch 8.1
Vocab
Consecutive vertices: vertices that are next to each
other or part of the same side.
Diagonal
A diagonal is a segment that connects 2 nonconsecutive edges.
Polygon Interior Angles Theorem
Theorem 8.1
What is the sum of the interior angles
of…
(n 2) 180
(3 2) 180 180
A triangle:
A quadrilateral:
A pentagon:
(5 2) 180 540
A hexagon:
(6 2) 180 720
A heptagon:
(4 2) 180 360
(7 2) 180 900
Corollary to Interior Angle Theorem
If I have the Sum of the interior angles how
do I figure out how many sides there are?
(n 2) 180 sum of angles
Given that the sum is 1800
(n 2) 180 1800
(n 2) 180 1800
180
180
n 2 10
n 12
If I have the Sum of the interior angles how
do I figure out how many sides there are?
(n 2) 180 sum of angles
Given that the sum is 1980
(n 2) 180 1980
(n 2) 180 1980
180
180
n 2 11
n 13
How would you find x?
What kind of figure is this?
What is the sum of the interior
angles?
108 121 59 x 360
288 x 360
x 72
What kind of figure is this?
What is the sum of the interior
angles of a pentagon?
(5 – 2)(180) = 540
110+92+100+84 + x = 540
386 + x = 540
x = 154
What kind of figure is it?
How do you find x?
What is the sum of the interior
angles of a heptagon?
(7 – 2)(180) = 900
145+112+99+133+156+2x+x = 900
645 + 3x = 900
3x = 255
x = 85
Finding exterior angles
How do you find x?
67 + 96 + 59 + 86 + x =
360
308 + x = 360
x = 52
Find x
X = 71
Page 510 #3 - 16
Word Problems
What is the measure of one exterior angle in a regular
triangle?
120 ̊
Recall that the sum of any convex
polygon’s exterior angles is 360.
Then divide by how many exterior
angles there are in the shape.
360 ÷ 3 = 120
What is the measure of an exterior
angle in a regular 10-gon?
360 ÷ 10 = 36 ̊
The measures of the exterior angles of
a convex pentagon are 54, 72, 2x, 3x
and x. What is the measure of the
largest angle?
The sum of the measure of the exterior angles
equals 360, so we’ll add the angles and find x.
54 + 72 + 2x + 3x + x = 360
126 + 6x = 360
6x = 234
X = 39
3x = 3(39) = 117
Find an interior and exterior angle for
a regular 11-gon
360 ÷ 11 = 32.73 ̊
X + 32.73 = 180
X = 147.27
How do you find how many sides a figure
has, when given one angle measure?
How do you find the sum of the interior angles?
(n – 2)180 = interior angle sum
If we have a regular figure all the angles are the
same, so we would divide the interior angle sum by
the number of sides, n, to find the measure of one
angle. (n 2)180
n
one angle measure
An interior angle of a regular polygon has
a measure of 150 ̊. How many sides does
the figure have?(n 2)180
n
one angle measure
(n 2)180
150 Multiply both sides by n!
n
(n 2)180
n
150 n
n
(n 2)180 150 n Distribute the 180!
180 n 360 150 n Subtract the 180n!
360 30 n
12 n
An interior angle of a regular polygon has
a measure of 120 ̊. How many sides does
the figure have?(n 2)180
n
one angle measure
(n 2)180
120 Multiply both sides by n!
n
(n 2)180
n
120 n
n
(n 2)180 120n Distribute the 180!
180 n 360 120 n Subtract the 180n!
360 60 n
6n
Find the measure of and interior and exterior angle of a
regular hexagon.
Find the measure of and interior and exterior angle of a
regular 20-gon.
A regular polygon has an angle measure of 108 ̊ how
many sides does the polygon have?