26. Open-Ended Sketch an equilateral polygon that is not equiangular.

27. Stage Design A theater-in-the-round allows for a play to have an audience on all sides. The diagram below shows a platform constructed for a theater-in-the-round stage. What type of regular polygon is the largest platform? Find the measure of each numbered angle.

    

28. Think About a Plan A triangle has two congruent interior angles and an exterior angle that measures 100. Find two possible sets of interior angle measures for the triangle.

    • How can a diagram help you?
    • What is the sum of the angle measures in a triangle?

Algebra Find the value of each variable.

The measure of an exterior angle of a regular polygon is given. Find the measure of an interior angle. Then find the number of sides.

32. 72
33. 36
34. 18
35. 30
36. x

Packaging The gift package below contains fruit and cheese. The fruit is in a container that has the shape of a regular octagon. The fruit container fits in a square box. A triangular cheese wedge fills each corner of the box.

37. Find the measure of each interior angle of a cheese wedge.
38. Reasoning Show how to rearrange the four pieces of cheese to make a regular polygon. What is the measure of each interior angle of the polygon?
39. Algebra A polygon has n sides. An interior angle of the polygon and an adjacent exterior angle form a straight angle.
    1. What is the sum of the measures of the n straight angles?
    2. What is the sum of the measures of the n interior angles?
    3. Using your answers above, what is the sum of the measures of the n exterior angles?
    4. What theorem do the steps above prove?

40. Reasoning Your friend says she has another way to find the sum of the interior angle measures of a polygon. She picks a point inside the polygon, draws a segment to each vertex, and counts the number of triangles. She multiplies the total by 180, and then subtracts 360 from the product. Does her method work? Explain.

    

41. Algebra The measure of an interior angle of a regular polygon is three times the measure of an exterior angle of the same polygon. What is the name of the polygon?

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