Question

7. Calculate the number of sides of a regular polygon whose interior angles are each 150°.
8. Calculate the number of sides of a regular polygon whose exterior angles are each 40°.
9. In a regular polygon each interior angle is 140° greater than each exterior angle.
Calculate the number of sides of the polygon.

Answer 1

Answer:

7.

Exterior angle

$180 - 150 = 30$

Number of sides

$\frac{total \: angle}{exterior} = \frac{360}{30} = 12$

Therefore, Number of sides is 12.

8.

Number of sides:

$\frac{total \: angle}{exterior} = \frac{360}{40} =9$

Therefore, Number of sides is 9.

9.

let exterior angle x

Interior angle = x + 140

x + 140 + x = 180

2x + 140 = 180

2x = 180 - 140 = 40

x = 20

Therefore, exterior angle is 20°

Number of sides:

$\frac{total \: angle}{exterior} = \frac{360}{20} =18$

Therefore, number of sides is 18.

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