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  No. of Sides  
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.
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 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 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) 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.
No. of Sides
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.
No. of Sides
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
No. of Sides
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
No. of Sides
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:
No. of Sides
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
Interior angle of the second polygon
Thnx