ANGLES IN A POLYGON
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Calculating Angles in Regular Polygons: Formulas and Examples, Exams of Analytical Geometry and Calculus
Learn how to find the interior and exterior angles of regular polygons using simple formulas and examples. Discover the relationship between interior and exterior angles and how to determine the number of sides given an angle measurement.
Typology: Exams
2021/2022
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ANGLES IN A POLYGON
WHAT IS A REGULAR POLYGON?
- A closed figure shape that has more than two sides.
- All angles and side are congruent
FORMULA
- What is I told you the sum of a shape that has 54 sides has an
interior sum of 9360 degrees?
- Do you know how I got that?
- Well, there’s a simple formula that we use to calculate the
interior sum of any polygon.
(n-2)180=Sum
*n means the number of sides on your shape.
LET’S TRY IT
Shape Number of Sides Subtract 2 Multiple by 180 Interior Sum Hexagon 6 6 - 2 = 4 4 x 180 720 Decagon 10 10 – 2 = 8 8 x 180 1440 Pentadecagon 15 15 – 2 = 13 13 x 180 2340 36 - gon 36 36 – 2 = 34 34 x 180 6120 Remember, you can always count the number of sides if given an image
FINDING JUST ONE ANGLE?
- What if we need to find out what one angle is?
- There is a formula for that!
Just take the interior sum and divide by the number of side.
EXAMPLE: FINDING JUST ANGLE ONE
(BLUE)
Shape Number of Sides Subtract 2 Multiple by 180 Interior Sum (degrees) Divide interior sum by the number of sides Each Interior angle (degrees) Hexagon 6 6 - 2 = 4 4 x 180 720 720 / 6 = 120 120 Decagon 10 10 – 2 = 8 8 x 180 1440 1440 / 10 = 144 144 Pentadecagon 15 15 – 2 = 13 13 x 180 2340 2340 / 15 = 156 156 36 - gon 36 36 – 2 = 34 34 x 180 6120 6120 / 36 = 170 170
FINDING MEASURES OF INTERIOR ANGLES OF POLYGONS Find the value of x 88 136 136 142 105 x
1st: Find (n-2)
2nd: Set up an equation
607 + x = 720
x = 113
o
EXTERIOR ANGLES
The sum of the exterior angles of any polygon is 360
o
.
HELPFUL HINTS
What is the relation
between an interior
angle and an
exterior angle?
2 1
They add to equal 180
o
USE THIS FACT!!!
FINDING THE NUMBER OF SIDES
OR N
- A regular polygon has an interior angle with a
measure of 140
o
. How many sides does it have?
1st Find an exterior angle
2nd Find n
IT IS A NONAGON!!
FORMULAS TO REMEMBER
- Sum of the interior angles of Polygon
- (n - 2)
- Sum of the exterior angles of any polygon
- 360 °
- Each interior angle of a regular polygon
- ((n - 2)180)/n
- Each exterior angle of a regular polygon
- 360/n