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Published byLouisa Grant Modified over 6 years ago
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A segment that joins two nonconsecutive vertices.
Drawing the diagonals from one vertex divides the polynomial into (n - 2) triangles, where n is the number of sides of the polygon. 360°
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6 6 720° 720°
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° ° nonagon
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71° ° ° ° 318° ° 42°
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Sum = (n - 2)180 Sum = (10 - 2)180 Sum = (8)180 Sum = 1440° Sum = (n - 2)180 1620 = (n - 2)180 9 = n - 2 11 = n 11-gon (hendecagon or undecagon) Sum = (n - 2)180 Sum = (5 - 2)180 Sum = (3)180 Sum = 540° m∠K + m∠L + m∠M + m∠N + m∠J = Sum x + x + 109° + 105° + 68° = 540° 2x + 282° = 540° 2x = 258° x = 129° m∠K = m∠L = 129°
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360° 360° 89° x ° ° ° ° 3x = 186° 62°
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2340° mInt∠ = (n - 2)180 _________ n 15 2340° ° ° 156° ° 360° ° mExt∠ = 360 ____ n 24°
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m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360° 66° + 77° + 82° + 62° + x = 360° 287° + x = 360° x = 73° mInt∠ = (n - 2)180 _________ n (9 - 2)180 9 mInt∠ = 140° mExt∠ = 360° ____ n 9 mExt∠ = 40
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