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The diagram shows a regular polygon. Work out the value of x.

The diagram shows a regular polygon. Work out the value of x.-example-1

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Answer:

x = 67.5 degrees

Explanation:

this is an octagon which has 8 sides

the sum of all interior angles can be found by taking the number of sides, reducing it by 2, and then multiplying by 180

(8-2)*180 = 6(180) = 1080

the 1080° must be split equally among all 8 angles because it is a 'regular' polygon

1080/8 = 135

however, 'x' represents half of each regular angle so it is 67.5 degrees

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