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

i) sides ii) sides iii) sides iv) sides

Answer:

Sides | Sum of the interior angles | |

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) right angles v) right angles vi) right angles

Answer:

Sum of the interior angles | ||

i) | ||

ii) | ||

iii) | ||

iv) | right angles | |

v) | right angles | |

vi) | right angles |

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

Hence not possible.

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

Answer:

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

Hence not possible.

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

Answer:

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

Hence possible.

The number of side

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

i) Pentagon ii) Hexagon iii) Heptagon iv) Octagon

Answer:

Polygon | Sides | Interior angles | Exterior Angle Interior Angle | |

i) | Pentagon | |||

ii) | Hexagon | |||

iii) | Heptagon | |||

iv) | Octagon |

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

i) sides ii) sides iii) sides iv) sides

Answer:

Sides | Exterior Angle Interior Angle | ||

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) sides ii) sides iii) sides iv) sides

Answer:

Exterior angle | Interior angles Exterior Angle | ||

i) | |||

ii) | |||

iii) | |||

iv) |

Question 11: Is it possible to have a regular polygon whose interior angles measure

Answer:

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

Hence not possible.

Question 12: Is it possible to have a regular polygon whose interior angles measure measures of a right angle.

Answer:

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

Hence possible

* *

Question 13: 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 * *

* *

Question 14: The ratio between the exterior angle and the interior angles is . Find the number of sides of the polygon.

Answer:

* *

Let the Exterior Angle and the Interior Angle be

Therefore Interior angle

Question 15: 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 16: Each exterior angle of a regular polygon is . Find the number of sides of the polygon.

Answer:

* *

Question 17: One angle of an Octagon is . 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 18: 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 19: 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

Question 20: Each interior angle of a regular polygon is . 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

Thnx