Question

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Answer 1

Part I : 2160°

Part II : 165°

Part III : 36 sides.

Part IV : 10 sides.

Explanation:

Part I : If the polygon has 14 sides, then the sum of all the interior angles of a polygon will be = (14 - 2) × 180° = 2160°. (Answer)

Part II : If the polygon has 24 sides, then the sum of all the interior angles of a polygon will be = (24 - 2) × 180° = 3960°.

Therefore, the measurement of each interior angles will be =
`(3960)/(24) = 165^(\circ)`. (Answer)

Part III : Given that 10° is each exterior angle of a polygon. So, each interior angle is (180 - 10) = 170°.

If the number of sides is n, then,

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

⇒ 10n = 360

⇒ n = 36 sides. (Answer)

Part IV : Sum of the all interior angles is 1440°.

If it has n sides, then (n - 2) \times 180 = 1440

⇒ n - 2 = 8

⇒ n = 10 (Answer)