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11.1 Angle Meas in Polygons

# 11.1 Angle Meas in Polygons - 11.1 Angle Measures in...

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Unformatted text preview: 11.1 Angle Measures in Polygons Polygons p. 661 If all the ∠ s iin a Δ add up to 180o n and all the ∠ s iin a quadrilateral add n up to 360o, what about a pentagon? up How about a hexagon? 2 * 180 = 3600 3 * 180 = 540o 4 * 180 = 720o Thm 11.1 – Polygon Interior ∠ s thm. Thm • The sum of the measures of the The interior ∠ s of a convex n-gon is of 180(n-2). 180(n-2). • Remember: n is the number of Remember: sides. sides. Ex: What is the sum of the Ex What measures of the interior ∠ s of a of dodecagon? dodecagon? First, how many sides does a First, dodecagon have? dodecagon n = 12 180(12-2) = 180(12-2) 180(10) = 1800o 1800 Ex: Find the value of x. Ex 114o xo 105o 135o Sum of all ∠ s is 540o Sum 114+105+102+135=456o 540 – 456 = 84o So, x = 84 102o Corollary to thm 11.1 Corollary • The measure of each interior ∠ of The a regular n-gon is regular 180(n − 2) n • This means the measure of ONE ∠ This ONLY!!! ONLY Ex: The measure of each interior Ex The ∠ of a regular polygon is 165o. How How many sides does the polygon have? many 180(n − 2) = 165 n 180(n-2) = 165n 180n-360 = 165n -360 = -15n 24 = n 24 sides Thm 11.2 – Polygon Exterior ∠ s Thm thm thm The sum of the measures of the The exterior ∠ s of a convex polygon, of one at each vertex, is 360o. one 2 1 m∠ 1 + m∠ 2 + m∠ 3 + m∠ 4 + m∠ 5 = 360o 3 5 4 Ex: Solve for y. Ex: y 2y 2y y 2y + y + 2y + y = 360 6y = 360 y = 60o Corollary to thm 11.2 Corollary • The measure of each exterior ∠ of The a regular n-gon is 360 n Ex: Solve for x. Ex: xo n=6 360/n = x 360/6 = x 60o = x This is a regular hexagon. Assignment Assignment ...
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