# date: sec 8-1 concept: angle measures in polygons objective: given a polygon, determine the measures...

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Date: Sec 8-1 Concept: Angle Measures in Polygons Objective: Given a polygon, determine the measures of angles as measured by a s.g. Slide 2 Sum of the measures of the interior angles in a polygon Sum of interior angles = (n-2)180, Where n = number of sides Slide 3 Example 1: Find the value of x S= (n-2)180 S=(5-2)180 S=540 114+105+102+135 = 456 540-456 =84 Slide 4 Example 2: Find the value of x X S= (n-2)180 S=(8-2)180 S=(6)180 S=1080 X= 1080/8 X = 135 Slide 5 Example 3: The sum of the measures of the interior angles in a convex polygon is given. Classify the polygon by the number of sides. A. 1980 B. 360 Slide 6 Example 4: Find the measure of each angle in a regular 11-gon (n-2)180 n (11-2)180 11 Each angle = 147.3 Slide 7 Example 5: The measure of each interior angle of a regular polygon is 165. How many sides does the polygon have? (n-2)180 = 165 n Cross mult. (n-2)180 = 165n 180n-360 = 165n -180n -360 = -15n -15 24 = n Slide 8 Sum of the exterior angles in a polygon is always 360 Example 6: What is the measure of each exterior angle in a regular hexagon? =360/6 =60 Slide 9 Example 7: Find the value of x Slide 10 Example 8: The measure of each exterior angle of a regular polygon is 40. How many sides does the polygon have? 360/40 =9 sides Slide 11 Example 9: Slide 12 Wrap-up: 1. How do you find the sum of the interior angles in a polygon? 2. How do you find the sum of the exterior angles in a polygon? 3. Why do you need to know this? Slide 13 Todays Work