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Packaging The nut container at the right has theshape of a regular octagon. It fits in a square box.A cheese wedge fills each corner of the box.
26. Find the measure of each angle of a cheese wedge.
27. Crit ical Thinking Show how to reaffangethe four pieces of cheese to make a regularpolygon. What is the measure of each angleof the polygon?
IJse a protractor. Sketch each type ofregular polygon.
Sample: dodecagon
Use the protractor to equally space 12 pointsaround a circle. (360" + 12 : 30",so mark a pointevery 30".) Connect these points to form a Iregular dodecagon.
@ opplv Your Skills
Connection
At a theater-in-the-round,seats are arranged so theaudience surrounds the staoe.
28. triangle
30. hexagon
(A) 25(F) s0
29. quadrilateral
31. octagon
a_e ) 115a-D) 160
The sum of the measures of the angles of a polygon with n sides is given. Find n.
3 2 . 1 8 0 33. 1080 34.1980 35. 2880
36. Multiple Choice In the figure at right, LB = LD andm L C : 1 3 0 . W h a t i s m L B ?
Hornework Video Tutor r@---
Visit : PHSchool.comWeb Code: bce-0305
162 chapter 3
37. Stage Design The diagram at the right shows platformsconstructed for a theater-in-the-round stage. Describe theIargest platform by the type of regular polygon it suggests.Find the measure of each numbered angle.
38. Error Analysis Miles said that he measured an angleof a regular polygon to be 130'. Explain why this resultis impossible.
39. Critical Thinking A triangle has two congruent angles and an exterior angle witlmeasure 100. Find two possible sets of measures for the angles of the triangle.
The measure of an exterior angle of a regular polygon is given. Find the measure oan interior angle, and find the number of sides.
40.72 41.36 42.78 43.30 44. x
45. Probability Find the probability that the measure of an angle of a regularru-gon is a positive integer if n is an integer and 3 < n -< 72.
ffi nO. Algebra A polygon has n sides. An interior angle of the polygon andan adjacent exterior angle form a straight angle.a. What is the sum of the measures of the n straight angles?b. What is the sum of the measures of the n interior angles?c. Using your answers above, what is the sum of the measures
ofthe n exterior angles?d. What theorem do the steos above lead to?
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