Transcript 11.1 Angles Measures in a Polygon

11.1 Angles Measures in
a Polygon
Sum of the angles in a
Triangle
180°
Quadrilateral 360°
Pentagon
540°
Hexagon
?
How to find the Sum,
Number of sides minus two times 180°
n  2180
Remember
Each angle of a Regular Polygon
Regular Polygons have all sides and angles
equal.
Each angle would be
n  2 180
n
Solve for x
Non regular polygon
114
102
x
135
105
Solve for x
102  105  114  135  x  (5  2) 180
114
102
x
135
105
456  x  540
x  84
Interior and External Angles of
Polygon
The External always add to 360°
Remember
How many sides?
If each interior angle of a regular polygon is
165°. The polygon had how many sides?
If you use the interior angle.
n  2 180  165
n
n  2 180  165n
180n  360  165n
 360  15n
n  24
How many sides?
If each interior angle of a regular polygon is
165°. The polygon had how many sides?
If you use the external angle. 180  165  15
360
 15
n
360  15n
n  24
Solve for y
2y
y
y
2y
Solve for y
2y
2 y  y  2 y  y  360
6 y  360
y  60
y
y
2y
Solve for x
x
Regular Hexagon
Solve for x
x
Regular Hexagon
n6
360
x
6
x  60
Homework
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