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7. 15-gon ANSWER: 24° 5-4 Polygons and Angles Find the sum of the interior angle measures of the polygon. 1. pentagon A tessellation is a repetitive pattern of polygons that fit together without overlapping and without gaps between them. For the tessellation, find the measure of each angle at the circled vertex. Then find the sum of the angles. ANSWER: 540° 2. 11-gon ANSWER: 1,620° 3. 13-gon ANSWER: 1,980° 8. ANSWER: 90°, 120°, 150°; 360° 4. The soccer ball below consists of repeating regular pentagons and hexagons. Find the measure of one interior angle of a pentagon. 9. ANSWER: 108° Find the measure of an exterior angle of each regular polygon. ANSWER: 60°, 90°, 90°, 120°; 360° Find the value of x in the figure. 10. 5. decagon ANSWER: 36° 6. 20-gon ANSWER: 18° ANSWER: 80 7. 15-gon ANSWER: 24° A tessellation is a repetitive pattern of polygons that fit together without overlapping and without gaps between them. For the tessellation, find the measure of each angle at eSolutions Manual - Powered Cognero the circled vertex.byThen find the sum of the angles. 11. Page 1 ANSWER: 130 ANSWER: 5-4 Polygons and Angles 80 11. ANSWER: 130° and 28° 13. Persevere with Problems How many sides does a regular polygon have if the measure of an interior angle is 160°? Justify your answer. ANSWER: = 160 18; (n – 2) 180 180n – 360 20n n ANSWER: 130 12. Model with Mathematics Refer to the graphic novel frame below. Find the measures of the two missing angles using properties of quadrilaterals and = 160n = 160n = = 360 18 Multiplication Property of Equality Distributive Property Properties of Equality Division Property of Equality parallel lines. 14. Reason Inductively If the number of sides of a polygon increases by 1, what happens to the sum of the measures of the interior angles? ANSWER: It increases by 180°. 15. Reason Inductively Devon drew a regular polygon and measured one of its interior angles. Explain why it is impossible for his angle measure to be 145°. ANSWER: Regular decagons have equal angles measuring 144° and regular 11-sided polygons have angles measuring 147.27°. 145° is between these two values so it cannot be the interior angle measure of a regular polygon. Find the sum of the interior angle measures of the polygon. 16. heptagon ANSWER: 900° ANSWER: 130° and 28° 17. 14-gon 13. Persevere with Problems How many sides does a regular polygon have if the measure of an interior angle is 160°? Justify your answer. ANSWER: 18; ANSWER: 2,160° 18. 24-gon = 160 (n – 2) = 160n Multiplication Property 180 of Equality 180n – = 160n Distributive Property 360 20n - Powered = 360 Properties of Equality eSolutions Manual by Cognero n = 18 Division Property of Equality ANSWER: 3,960° Find the measure of one interior angle in the regular polygon. Round to the nearest tenth if necessary. 19. nonagon Page 2 ANSWER: 140° 2,160° 18. 24-gon ANSWER: 5-4 Polygons and Angles 3,960° Find the measure of one interior angle in the regular polygon. Round to the nearest tenth if necessary. 19. nonagon ANSWER: 140° 25. 18-gon ANSWER: 20° 26. The surface of the dome of Spaceship Earth in Orlando consists of repeating equilateral triangles as shown. Find the measure of each angle in each outlined triangle. Then make a conjecture about the interior angle measures in equilateral triangles of different sizes. 20. decagon ANSWER: 144° 21. 19-gon ANSWER: 161.1° 22. 16-gon ANSWER: 157.5° Find the measure of an exterior angle of the regular polygon. 23. nonagon ANSWER: 40° 24. 12-gon ANSWER: 30° 25. 18-gon ANSWER: 20° ANSWER: The measure of each angle in each outlined triangle is 60°. If a triangle is equilateral, the measure of each angle will be 60° regardless of the size of the triangle. 27. Justify Conclusions What is the sum of the interior angles of nonregular hexagons? Explain your reasoning to a classmate. ANSWER: Sample answer: The sum of the interior angles will still be 720° because even though the figures are not regular, they are still hexagons. 26. The surface of the dome of Spaceship Earth in Orlando consists of repeating equilateral triangles as shown. Find the measure of each angle in each outlined triangle. Then make a conjecture about the interior angle measures in equilateral triangles of different sizes. eSolutions Manual - Powered by Cognero 28. After the first two folds of an origami paper design, the paper is shaped like a square with two isosceles triangles removed from two adjacent corners. Page 3 Angles AED and BCD are congruent. Select the correct values to complete the model below to find ANSWER: Sample answer: The sum of the interior angles will 5-4 Polygons and Angles still be 720° because even though the figures are not regular, they are still hexagons. 28. After the first two folds of an origami paper design, the paper is shaped like a square with two isosceles triangles removed from two adjacent corners. ANSWER: 2 ∙ x + 3 ∙ 90 = 540 m∠AED = 135° 29. Fill in each box to make each statement true. a. The sum of the interior angle measures of a quadrilateral is _________. b. The sum of the interior angle measures of a(n) _________ is 720°. c. The sum of the interior angle measures of an octagon is _________. d. The sum of the interior angle measures of a(n) _________ is 1,620°. Angles AED and BCD are congruent. Select the correct values to complete the model below to find the measure of angle AED. x 180 2 360 3 540 45 720 90 ∙ + ∙ = Classify the pair of angles as complementary, supplementary, or neither. 30. angle 1: 35° angle 2: 55° What is m∠AED? ANSWER: 2 ∙ x + 3 ∙ 90 ANSWER: a. The sum of the interior angle measures of a quadrilateral is 360°. b. The sum of the interior angle measures of a(n) hexagon is 720°. c. The sum of the interior angle measures of an octagon is 1,080°. d. The sum of the interior angle measures of a(n) 11gon is 1,620°. = 540 ANSWER: complementary m∠AED = 135° 29. Fill in each box to make each statement true. a. The sum of the interior angle measures of a quadrilateral is _________. b. The sum of the interior angle measures of a(n) _________ is 720°. c. The sum of the interior angle measures of an octagon is _________. d. The sum of the interior angle measures of a(n) _________ is 1,620°. 31. angle 1: 62° angle 2: 108° ANSWER: neither Find the value of x in the triangle. 32. ANSWER: a. The sum of the interior angle measures of a quadrilateral is 360°. b. The sum of the interior angle measures of a(n) hexagon is 720°. c. The sum of the interior angle measures of an octagon is 1,080°. d. The sum of the interior angle measures of a(n) 11eSolutions Manual - Powered by Cognero gon is 1,620°. Classify the pair of angles as complementary, ANSWER: 51 33. Page 4 ANSWER: 5-4 Polygons and Angles 51 33. ANSWER: 26 eSolutions Manual - Powered by Cognero Page 5