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 ngon is of 180(n2). 180(n2). • 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(122) = 180(122) 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 ngon 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(n2) = 165n 180n360 = 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 ngon 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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 Spring '11
 Jackson
 ex, Regular polygon, Thm thm thm

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