5.3 Angles in Polygons.notebook
November 27, 2014
5.3 Angles in Polygons.notebook
November 27, 2014
quadrilateral
trapezoid
parallelogram
rectangle
square
rhombus
kite
isosceles
trapezoid
5.3 Angles in Polygons.notebook
5.3 Angles in Polygons
What is the sum of the interior angles of a polygon?
What is the sum of the exterior angles of a polygon?
November 27, 2014
5.3 Angles in Polygons.notebook
Consider the sum of the angles in a quadrilateral?
Pentagon
Hexagon
Heptagon
Octagon
November 27, 2014
5.3 Angles in Polygons.notebook
The sum of the exterior angles of a convex polygon is: _______
The sum of the interior angles of a polygon with n sides is: ____________
November 27, 2014
5.3 Angles in Polygons.notebook
November 27, 2014
Regular polygon: polygon with equal sides and equal interior angles.
Ex. 1 Determine the measure of each exterior angle in a regular 11‐sided polygon.
e
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e
e
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5.3 Angles in Polygons.notebook
November 27, 2014
Ex. 2 Determine the measure of each interior angle in a regular 15‐sided polygon.
METHOD #1
METHOD #2
5.3 Angles in Polygons.notebook
November 27, 2014
Ex. 3 Determine the value of x.
x
x + 20
x + 5
x ‐ 15
x ‐ 10
x + 6
x + x + 20 + x ‐ 15 + x + 6 + x ‐ 10 + x + 5 = 720°
6x + 6 = 720°
6x = 714°
x = 119°
5.3 Angles in Polygons.notebook
November 27, 2014
Ex. 4 The interior angles of a regular polygon add to 1440°. How many sides does the polygon have?
∴ The polygon has 10 sides.
Ex: 5 How many sides does a polygon have if each of its interior angles measures 162o?
METHOD #1
Sum = 180(n ‐ 2)
162n = 180(n ‐ 2)
162n = 180n ‐ 360
162n ‐ 180n = ‐360
‐ 18n = ‐360
‐18 ‐18
n = 20
METHOD #2
Exterior Angles = 180 ‐ 162
= 18o # of Angles (n) = 360
18
n = 20
5.3 Angles in Polygons.notebook
November 27, 2014
Homework:
Page 390 # 1-2, 3a, 7, 10, 11, 12
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