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Name: Geometry Period _______ 4-6 HW Date ________ Directions: For each, choose a question either from the left or right column. Each column helps you practice the same content, but the right column allows you to challenge yourself. 1) Carlotta is designing a garden for her backyard. She wants a flower bed shaped like a regular octagon. Find the sum of the measures of the interior angles of the octagon. 1) Find the measure of each interior angle: 2) The measure of an interior angle of a regular polygon is 140°. Find the number of sides in the polygon. 2) The measure of an interior angle of a regular polygon 1 is 157 o. Find the number of sides in the polygon. 3) The pentagon building in Washington DC was designed to resemble a regular pentagon. Find the measure of an interior angle. 3) Find an expression to represent the sum of the measures of the interior angles of the following convex polygon: 2 4π₯ β πππ (as opposed to a 29-gon that has 29 sides) 4) What is the measure, in degrees, of each exterior angle of a regular hexagon? 4) What is the measure, in degrees, of each exterior angle of a regular n-sided figure? 5) What is the measure of the sum of the exterior angles of a dodecagon (12 sides)? 5) What is the sum of the exterior angles of a polygon with 5,128 sides? 6) The measure of each exterior angle of a regular polygon is 60. How many sides does the polygon have? What is the name of the polygon? 6) Jack says the measure of each exterior angle of a regular polygon is 75. Jill says that isnβt possible. Who is right? Explain. Challenge: James and Nicole were asked to find the measure of a single angle in a regular polygon on a test. James used the formula a= 180(πβ2) π , while Nicole first found the exterior angle and then founds itβs supplement. Do James, Nicole, or both get the question right? How do you know?