find angle measure s in polygons
DESCRIPTION
Find Angle Measure s 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 non-consecutive edges. Polygon Interior Angles Theorem. Theorem 8.1. - PowerPoint PPT PresentationTRANSCRIPT
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FIND ANGLE MEASURES IN POLYGONS
Ch 8.1
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Vocab
Consecutive vertices: vertices that are next to each other or part of the same side.
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Diagonal
A diagonal is a segment that connects 2 non-consecutive edges.
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Polygon Interior Angles Theorem Theorem 8.1
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What is the sum of the interior angles of… A triangle:
A quadrilateral:
A pentagon:
A hexagon:
A heptagon:
180)2( n180)23( 180
180)24( 360
180)25( 540
180)26( 720
180)27( 900
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Corollary to Interior Angle Theorem
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If I have the Sum of the interior angles how do I figure out how many sides there are?
anglesofsumn 180)2(1800issumthethatGiven
1800180)2( n
180
1800
180
180)2(
n
102n12n
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If I have the Sum of the interior angles how do I figure out how many sides there are?
anglesofsumn 180)2(1980issumthethatGiven
1980180)2( n
180
1980
180
180)2(
n
112n13n
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How would you find x?
What kind of figure is this?What is the sum of the interior angles?
36059121108 x
360288 x72x
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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 = 540386 + x = 540
x = 154
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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 = 900645 + 3x = 900
3x = 255x = 85
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Finding exterior angles
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How do you find x?
67 + 96 + 59 + 86 + x = 360
308 + x = 360
x = 52
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Find x
X = 71
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Word Problems
120 ̊
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What is the measure of an exterior angle in a regular 10-gon?360 ÷ 10 = 36 ̊
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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
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Find an interior and exterior angle for a regular 11-gon 360 ÷ 11 = 32.73 ̊
X + 32.73 = 180
X = 147.27
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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.
measureangleonen
n
180)2(
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An interior angle of a regular polygon has a measure of 150 . ̊How many sides does the figure have?
measureangleonen
n
180)2(
150180)2(
n
nMultiply both sides by n!
nn
nn
150
180)2(
nn 150180)2(
nn 150360180 Distribute the 180!
n30360 n12
Subtract the 180n!
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An interior angle of a regular polygon has a measure of 120 . ̊How many sides does the figure have?
measureangleonen
n
180)2(
120180)2(
n
nMultiply both sides by n!
nn
nn
120
180)2(
nn 120180)2( nn 120360180
Distribute the 180!
n60360 n6Subtract the 180n!
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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?