Question 1: Calculate the sum of all the interior angles of a polygon having:

(i) | ||

(ii) | ||

(iii) | ||

(iv) |

Question 2: Find the number of sides of a polygon, the sum of whose interior angles is:

(i) | ||

(ii) | ||

(iii) | ||

(iv) | ||

(v) | ||

(vi) |

Question 3: The sides of a hexagon are produced in order. If the measure of the exterior angles so obtained are . Find the value of x and the measure of each exterior angle of the hexagon.

Answer:

Sum of the interior angles of hexagon

Now substitute the value of in the expressions of all the sides we get:

Question 4: Is it possible to have a polygon whose sum of interior angles is

Answer:

No. Let us calculate the number of sides of this polygon.

No. of Sides which is not an integer.

Hence not possible.

Question 5: Is it possible to have a polygon, the sum of whose interior angles is 7 right angles.

Answer:

No. Let us calculate the number of sides of this polygon.

No. of Sides

Hence not possible.

Question 6: Is it possible to have a polygon, the sum of whose interior angles is 14 right angles. If yes, how many sides does this polygon have?

Answer:

Yes. Let us calculate the number of sides of this polygon.

No. of Sides

Hence possible.

The number of side

Question 7: Find the measure of each angle of a regular polygon

(i) | ||||

(ii) | ||||

(iii) | ||||

(iv) |

Question 8: Find the measure of each angle of a regular polygon having

(i) | |||

(ii) | |||

(iii) | |||

(iv) | |||

(v) | |||

(vi) | |||

(vii) |

Question 9: Find the number of sides of a regular polygon each of whose exterior angles are:

(i) | |||

(ii) | |||

(iii) | |||

(iv) |

Question 10: Is it possible to have a regular polygon whose interior angles measure 130°

Answer:

No. Let us calculate the number of sides of this polygon.

No. of Sides

Hence not possible.

Question 11: Is it possible to have a regular polygon whose interior angles measure measures 1 3/4 of a right angle.

Answer:

Yes. Let us calculate the number of sides of this polygon.

No. of Sides

Hence possible

* *

Question 12: Find the number of sides of a regular polygon, if its interior angle is equal to exterior angle.

Answer:

* *

This means that each of the interior and the exterior angles * *

No. of Sides

* *

Question 13: The ratio between the exterior angle and the interior angles is 2:7. Find the number of sides of the polygon.

Answer:

* *

Let the Exterior Angle and the Interior Angle be

Therefore Interior angle

No. of Sides

Question 14: The sum of all the interior angles of a regular polygon is twice the sum of exterior angles. Find the number of sides of the polygon.

Answer:

Sum of Interior Angles

Sum of Exterior Angles

Given Sum of Interior Angles

Question 15: Each exterior angle of a regular polygon is . Find the number of sides of the polygon.

Answer:

* *

No. of Sides

Question 16: One angle of an Octagon is 100. And all the other seven angles are equal. What is the measure of each one of the equal angles?

Answer:

One angle given

Let each of the equal angles

Sum of Interior Angles

Each of the equal angles

Question 17: The angles of Septagon are in the ratio of . Find the smallest angle.

Answer:

Sum of Interior Angles

Let the angles be

Therefore

Hence the angles are

The smallest angle is

Question 18: Two angles of a polygon are right angles and each of the other angles is . Find the number of sides of the polygon.

Answer:

Let the number of sides

Sum of Exterior Angles

or

Question 19: Each interior angle of a regular polygon is 144. Find the interior angle of a polygon, which has double the number of sides as the first polygon.

Answer:

Let the number of sides of the first polygon

Therefore the number of sides of the second polygon

Interior angle of the second polygon