Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

1) Blank 1: 120°

Blank 2: 60°

Blank 3: 90°

Blank 4: 90°

Blank 5: 12

2) 72

3) 45

Explanation:

Measure of one interior angle of a polygon with n sides is :
`((n-2)*180)/(n)`

Measure of one exterior angle of a polygon with n sides is:

`180 - ((n-2)*180)/(n)\\\\= (360)/(n)`

1)

Blank 1:

n = 6

interior angle :

`((6-2)*180)/(6)\\\\= (4*180)/(6)\\\\=(720)/(6)\\\\=120`

Blank 2:

n = 6

exterior angle:

`(360)/(n)\\\\= (360)/(6)\\\\=60`

Blank 3:

n = 4

`((4-2)*180)/(4)\\\\= (2*180)/(4)\\\\=(360)/(4)\\\\=90`

Blank 4:

n = 4

exterior angle:

`(360)/(n)\\\\= (360)/(4)\\\\=90`

Blank 5:

In the picture, one interior angle of the gree polygon is ∠A + ∠B

where ∠A is one exterior angle of the hexagon and ∠B is one exterior angle of the quad

The interior angle of the green polygon:

∠A + ∠B

= 60 + 90

= 150

Let the green polygon have n sides

`\implies ((n-2)*180)/(n) = 150\\\\\implies (n-2)*180 = 150n\\\\\implies 180n - 360 = 150n\\\\\implies 180n - 150n = 360\\\\\implies 30n = 360\\\\\implies n = (360)/(30)\\\\\implies n = 12`

2)

One rotation is 360°

Since the number of sides is 5,

min. rotation =
`(360)/(5)`

= 72

3)

One rotation is 360°

Since the number of sides is 8,

min. rotation =
`(360)/(8)`

= 45