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

(i) |
||

(ii) |
||

(iii) |
||

(iv) |

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

(i) | ||

(ii) | ||

(iii) | ||

(iv) | ||

(v) | ||

(vi) |

Q.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:

Q.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.

Q.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.

Q.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

Q.7. Find the measure of each angle of a regular polygon

(i) | ||||

(ii) | ||||

(iii) | ||||

(iv) |

Q.8. Find the measure of each angle of a regular polygon having

(i) | |||

(ii) | |||

(iii) | |||

(iv) | |||

(v) | |||

(vi) | |||

(vii) |

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

(i) | |||

(ii) | |||

(iii) | |||

(iv) |

Q.10. Is it possible to have a regular polygon whose interior angles measure 130°

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

No. of Sides

Hence not possible.

Q.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

* *

Q.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

* *

Q.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

Q.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

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

Answer:

* *

No. of Sides

Q.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

Q.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

Q.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

Q.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.

Let the number of sides of the first polygon

Therefore the number of sides of the second polygon

Interior angle of the second polygon