If each interior angle of a regular polygon measure 135- then it has - sides-

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Standard VI

Mathematics

Regular Polygon and Its Properties

If each inter...

Question

If each interior angle of a regular polygon measure $135^{\circ},$ then it has __ sides.

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Solution

The correct option is B
8

Let the number of sides of the regular polygon = n
We know $i^{\circ} + e^{\circ} = 180^{\circ} ∴ e^{\circ} = 180^{\circ} ∴ e^{\circ} = 180 - 135^{\circ} e^{\circ} = 45^{\circ} n = \frac{360^{\circ}}{e^{\circ}} n = \frac{360^{\circ}}{45^{\circ}} n = 8$

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If each interior angle of a regular polygon measure 135∘, then it has __ sides.

The correct option is B 8 Let the number of sides of the regular polygon = n We know i∘+e∘=180∘∴e∘=180∘∴e∘=180−135∘e∘=45∘n=360∘e∘n=360∘45∘n=8

If each interior angle of a regular polygon measure $135^{\circ},$ then it has __ sides.

The correct option is B
8

Let the number of sides of the regular polygon = n
We know $i^{\circ} + e^{\circ} = 180^{\circ} ∴ e^{\circ} = 180^{\circ} ∴ e^{\circ} = 180 - 135^{\circ} e^{\circ} = 45^{\circ} n = \frac{360^{\circ}}{e^{\circ}} n = \frac{360^{\circ}}{45^{\circ}} n = 8$