Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

QUESTIONS BELOW
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Answer 1

1) 162

2)

1) b) 120

2) e) 90

3) a) 72

4) c) 60

3) 49

Explanation:

1) n = 20

each interior angle is given by:

`((n-2)*180)/(n)\\ \\= ((20-2)*180)/(20)\\\\=(18*180)/(20)\\\\=162`

2)

Measure of one exterior angle of a polygon with n sides is :
`(360)/(n)`

(1) triangle : 3 sides

exterior = 360/3 = 120

(2) quad : 4 sides

exterior = 360/4 = 90

(3) pentagon : 5 sides

exterior = 360/5 = 72

(4) hexagon : 6 sides

exterior = 360/6 = 60

3) The shape isa quadrilateral (n = 4)

Sum of interior angles is:

(n-2)* 180

= (4 - 2)*180

= 2*180

= 360

⇒ (2x + 15) + (3x - 20) + (x + 15) + (x + 7) = 360

⇒ 7x + 17 = 360

⇒ 7x = 360 - 17

⇒ 7x = 343

⇒ x =
`(343)/(7)`

⇒ x = 49