The polygon in which the sum of all exterior angles is equal to the sum of interior angles is called ____.

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Detailed Solution

The polygon in which the sum of all exterior angles is equal to the sum of interior angles is called quadrilateral.
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In quadrilateral the sum of all four interior angles is

n − 2 × 180 ° = 4 − 2 × 180 ° = 360 °

.
Then

∠ w + ∠ x + ∠ y + ∠ z = 360 °

.
Now finding the sum of the all-exterior angles:

= 180 ° − ∠ w + 180 ° − ∠ x + 180 ° − ∠ y + 180 ° − ∠ z = 720 ° − ∠ w − ∠ x − ∠ y − ∠ z = 720 ° − ∠ w + ∠ x + ∠ y + ∠ z = 720 ° − 360 ° = 360 °

Therefore, the correct answer is quadrilateral.

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