5-4 Polygons and Angles. Find the sum of the interior angle measures of the polygon. 1. pentagon ANSWER: gon ANSWER: 1,620
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1 Find the sum of the interior angle measures of the polygon. 1. pentagon 540 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 gon 1, gon 1, The soccer ball below consists of repeating regular pentagons and hexagons. Find the measure of one interior angle of a pentagon , 120, 150 ; Find the measure of an exterior angle of each regular polygon. 5. decagon gon gon , 90, 90, 120 ; 360 Find the value of x in the figure esolutions Manual - Powered by Cognero Page 1
2 Model with Mathematics Refer to the graphic novel frame below. Find the measures of the two missing angles using properties of quadrilaterals and parallel lines. 13. Persevere with Problems How many sides does a regular polygon have if the measure of an interior angle is 160? Justify your answer. 18; = 160 (n 2) = 160n Multiplication Property 180 of Equality 180n = 160n Distributive Property n = 360 Properties of Equality n = 18 Division Property of Equality 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? It increases by 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. Regular decagons have equal angles measuring 144 and regular 11-sided polygons have angles measuring is between these two values so it cannot be the interior angle measure of a regular polygon. 130 and 28 Find the sum of the interior angle measures of the polygon. 16. heptagon gon 2, gon 3,960 esolutions Manual - Powered by Cognero Page 2
3 Find the measure of one interior angle in the regular polygon. Round to the nearest tenth if necessary. 19. nonagon 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 gon gon Find the measure of an exterior angle of the regular polygon. 23. nonagon gon gon 20 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. Sample answer: The sum of the interior angles will still be 720 because even though the figures are not regular, they are still hexagons. esolutions Manual - Powered by Cognero Page 3
4 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. 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 = What is m AED? 2 x = 540 m AED = 135 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) 11- gon is 1,620. Classify the pair of angles as complementary, supplementary, or neither. 30. angle 1: 35 angle 2: 55 complementary 31. angle 1: 62 angle 2: 108 neither Find the value of x in the triangle esolutions Manual - Powered by Cognero Page 4
5 esolutions Manual - Powered by Cognero Page 5
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