Question

For* 15-16 find the number of sides if a polygon has the given measure for each interior angle,

170
15 n=a) 21 b) 24 c) 30 4) 36 )42
162
16. n = a) 16 D) 20 c)24 d) 28 ) 32
60
For #17 - 24. determine the sum of the interior angles then find the missing angle.
17. sum = a) 120 b) 140 c) 160
d) 180 e) 200
18 x= a) 40 b) 50 c)60
d) 70 e) 80
X
70
120
19 Sum = a) 300 b) 330 C) 360 d) 380 e) 410
20 X a) 50 b) 60 с) 75 d) 80 e) 85
90
90
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Answer 1

15. d) 36

16. b) 20

17. d) 180

18. b) 50

19. c) 360

20. b) 60

Explanation:

To find the number of sides a polygon has giving an interior angle, use the equation:

(number of sides - 2)*180/(number of sides) = measure of interior angle

15. (n = number of sides)

((n-2)*180)/n = 170

180n-360 = 170n

10n = 360

n = 36 (d)

16. (n = number of sides)

((n-2)*180)/n = 162

180n-360 = 162n

18n = 360

n = 20 (b)

17. The sum of the interior angles of a triangle is always 180 (d)

18. 180-60-70 = 50 (b)

19. The sum of the interior angles of a quadrilateral is always 360 (c)

20. 360-120-90-90 = 60 (b)