Worksheet Solutions: Polygons | Know Your Aptitude Class 6 To 8 - Class 8 PDF Download

Section A: Fill in the Blanks

Q1: The sum of the interior angles of a polygon with n sides is given by the formula _________.

Ans: (n - 2) * 180 degrees.
Explanation: This formula can be used to find the sum of the interior angles of any polygon.

Q2: A polygon with three sides is called a _________.

Ans: triangle.
Explanation: Triangles are the simplest type of polygon with three sides.

Q3: In a regular polygon, all sides and angles are _________.

Ans: equal.
Explanation: Regular polygons have equal side lengths and equal angles.

Q4: A polygon with six sides is called a _________.

Ans: hexagon.
Explanation: Hexagons have six sides.

Q5: The sum of the exterior angles of any polygon is always _________.

Ans: 360 degrees.
Explanation: The sum of the exterior angles of any polygon is constant and equal to 360 degrees.

Section B: Match the Column

Ans:

Section C: True or False

Q1: The sum of the interior angles of a triangle is 180 degrees. _________

Ans: True
Explanation: The sum of the interior angles of a triangle is always 180 degrees.

Q2: A regular polygon can have an odd number of sides. _________

Ans: False
Explanation: A regular polygon must have an even number of sides.

Q3: The sum of the interior angles of a hexagon is 720 degrees. _________

Ans: True
Explanation: The sum of the interior angles of a hexagon is 720 degrees.

Q4: A quadrilateral has four equal angles. _________

Ans: False
Explanation: A quadrilateral can have unequal angles.

Q5: The sum of the exterior angles of any polygon is 360 degrees. _________

Ans: True
Explanation: The sum of the exterior angles of any polygon is always 360 degrees.

Section D: Angles in Polygons

Q1: Find the sum of the interior angles of a polygon with 10 sides.

Ans: 1440 degrees.
Explanation: Using the formula (n - 2) * 180, substitute n = 10 to get (10 - 2) * 180 = 8 * 180 = 1440 degrees.

Q2: If the sum of the interior angles of a polygon is 1440 degrees, how many sides does the polygon have?

Ans: The polygon has 9 sides.
Explanation: Rearranging the formula (n - 2) * 180 = 1440, we have (n - 2) * 180 = 1440. Solving for n, (n - 2) = 8, n = 8 + 2 = 10. Therefore, the polygon has 10 sides.

Q3: The measure of each interior angle of a regular hexagon.

Ans: Each interior angle measures 120 degrees.
Explanation: A regular hexagon has 6 equal angles. To find the measure of each angle, divide the sum of the interior angles (720 degrees) by 6.

Q4: The measure of each exterior angle of a regular pentagon.

Ans: Each exterior angle measures 72 degrees.
Explanation: A regular pentagon has 5 equal angles. To find the measure of each angle, divide the sum of the exterior angles (360 degrees) by 5.

Q5: The sum of the interior angles of a polygon is 2340 degrees. How many sides does the polygon have?

Ans: The polygon has 15 sides.
Explanation: Rearranging the formula (n - 2) * 180 = 2340, we have (n - 2) * 180 = 2340. Solving for n, (n - 2) = 13, n = 13 + 2 = 15. Therefore, the polygon has 15 sides.