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Splash Screen. Five-Minute Check (over Chapter 5) Then/Now New Vocabulary Theorem 6.1: Polygon Interior Angles Sum Example 1: Find the Interior Angles Sum of a Polygon Example 2: Real-World Example: Interior Angle Measure of Regular Polygon

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**Five-Minute Check (over Chapter 5)**Then/Now New Vocabulary Theorem 6.1: Polygon Interior Angles Sum Example 1: Find the Interior Angles Sum of a Polygon Example 2: Real-World Example: Interior Angle Measure of Regular Polygon Example 3: Find Number of Sides Given Interior Angle Measure Theorem 6.2: Polygon Exterior Angles Sum Example 4: Find Exterior Angle Measures of a Polygon Lesson Menu**A**B C D Write an inequality relating mABD and mCBD. A.mABD < mCBD B.mABD ≤ mCBD C.mABD > mCBD D.mABD = mCBD 5-Minute Check 5**A**B C D Write an equation that you can use to find the measures of the angles of the triangle. A.x – 5 + 3x = 180 B.x – 5 + 3x + 111 = 180 C.x – 5 + 3x = 69 D.x – 5 + 3x = 111 5-Minute Check 6**You named and classified polygons. (Lesson 1–6)**• Find and use the sum of the measures of the interior angles of a polygon. • Find and use the sum of the measures of the exterior angles of a polygon. Then/Now**diagonal**Vocabulary**Find the Interior Angles Sum of a Polygon**A. Find the sum of the measures of the interior angles of a convex nonagon. A nonagon has nine sides. Use the Polygon Interior Angles Sum Theorem to find the sum of its interior angle measures. (n – 2) ● 180 = (9 – 2) ● 180 n = 9 = 7 ● 180 or 1260 Simplify. Answer: The sum of the measures is. Example 1A**Since the sum of the measures of the interior angles is**Write an equation to express the sum of the measures of the interior angles of the polygon. Find the Interior Angles Sum of a Polygon B. Find the measure of each interior angle of parallelogram RSTU. Step 1 Find x. Example 1B**Find the Interior Angles Sum of a Polygon**Sum of measures of interior angles Substitution Combine like terms. Subtract 8 from each side. Divide each side by 32. Example 1B**Find the Interior Angles Sum of a Polygon**Step 2 Use the value of x to find the measure of each angle. m R = 5x = 5(11) or 55 m S = 11x + 4 = 11(11) + 4 or 125 m T = 5x = 5(11) or 55 m U = 11x + 4 = 11(11) + 4 or 125 Answer: Example 1B**A**B C D A. Find the sum of the measures of the interior angles of a convex octagon. A. 900 B. 1080 C. 1260 D. 1440 Example 1A**A**B C D B. Find the value of x. A.x = 7.8 B.x = 22.2 C.x = 15 D.x = 10 Example 1B**Interior Angle Measure of Regular Polygon**ARCHITECTUREA mall is designed so that five walkways meet at a food court that is in the shape of a regular pentagon. Find the measure of one of the interior angles of the pentagon. Example 2**Interior Angle Measure of Regular Polygon**Understand Look at the diagram of the situation. The measure of the angle of a corner in between two walkways is the interior angle of a regular pentagon. Plan Use the Polygon Interior Angles Sum Theorem to find the sum of the measures of the angles. Since the angles of a regular polygon are congruent, divide this sum by the number of angles to find the measure of each interior angle. Example 2**Interior Angle Measure of Regular Polygon**Solve Find the sum of the interior angle measures. (n – 2) ● 180 = (5 – 2) ● 180 n = 5 = 3 ● 180 or 540 Simplify. Find the measure of one interior angle. Substitution Divide. Example 2**Interior Angle Measure of Regular Polygon**Answer: Check To verify that this measure is correct, use a ruler and a protractor to draw a regular pentagon using 108 as the measure of each interior angle. The last side drawn should connect with the beginning point of the first segment drawn. Example 2**A**B C D A pottery mold makes bowls that are in the shape of a regular heptagon. Find the measure of one of the interior angles of the bowl. A. 130° B. 128.57° C. 140° D. 125.5° Example 2**Find Number of Sides Given Interior Angle Measure**The measure of an interior angle of a regular polygon is 150. Find the number of sides in the polygon. Use the Interior Angle Sum Theorem to write an equation to solve for n, the number of sides. S = 180(n – 2) Interior Angle Sum Theorem (150)n = 180(n – 2) S = 150n 150n = 180n – 360 Distributive Property 0 = 30n – 360 Subtract 150n from each side. Example 3**Find Number of Sides Given Interior Angle Measure**360= 30n Add 360 to each side. 12= n Divide each side by 30. Answer: The polygon has sides. Example 3**A**B C D The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon. A. 12 B. 9 C. 11 D. 10 Example 3**Find Exterior Angle Measures of a Polygon**A. Find the value of x in the diagram. Example 4A**Find Exterior Angle Measures of a Polygon**Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x. 5x + (4x – 6) + (5x – 5) + (4x + 3) + (6x – 12) + (2x + 3) + (5x + 5) = 360 (5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(–6) + (–5) + 3 + (–12) + 3 + 5] = 360 31x – 12 = 360 31x = 372 x = Answer: x = Example 4A**Find Exterior Angle Measures of a Polygon**B. Find the measure of each exterior angle of a regular decagon. A regular decagon has 10 congruent sides and 10 congruent angles. The exterior angles are also congruent, since angles supplementary to congruent angles are congruent. Let n = the measure of each exterior angle and write and solve an equation. 10n = 360 Polygon Exterior Angle Sum Theorem n = 36 Divide each side by 10. Answer: The measure of each exterior angle of a regular decagon is Example 4B**A**B C D A. Find the value of x in the diagram. A. 10 B. 12 C. 14 D. 15 Example 4A**A**B C D B. Find the measure of each exterior angle of a regular pentagon. A. 72 B. 60 C. 45 D. 90 Example 4B

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