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Which of the following are possible measures of the interior angles of a regular polygon? If possible, how many sides does the polygon have: 90°, 100°, 110° 125°, 150°, 175°.

Respuesta :

Answer:

90°- 4sides, 150°- 12sides, 175°- 72sides

Step-by-step explanation:

Theorem: Int. ∠ in reg. polyg. - 180°(n-2)/n

1. 180°(n-2)/n = 90°

    n=4 → Possible

2. 180°(n-2)/n = 100°

    n=9/2 → Not Possible

3. 180°(n-2)/n = 110°

    n=36/7 → Not Possible

4. 180°(n-2)/n = 125°

    n=72/11 → Not Possible

5. 180°(n-2)/n = 150°

    n=12 → Possible

6. 180°(n-2)/n = 175°

    n=72 → Possible

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