8th Polygons Solved Questions Paper[CBSE Maths]

1.Q. Find the number of diagonals in an octagon?

Ans: Number Of Diagonals Of Polygon = n(n-3) / 2     

Where n is Number Of Sides

Here n = 8

Diagonals= [8(8-3)5]/2 = 20

2.Q. Find the number of sides of a polygon whose each exterior angle is 45⁰ .

Ans: Measure of Each Exterior Angle of a Polygon = 360/n

Each Exterior Angle = 45

45 = 360/n

Number of Sides = 360/45 =8

So Number of Sides = 8

3. Q. The sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles. Determine the number of sides of the polygon.

Ans: sum of the interior angles of a regular polygon is 3 times the sum of its exterior angles.

We know that in a regular polygon sum of all the exterior angles = 360°

Therefore, sum of interior angles = 3 × 360° = 1080°

Again, we have sum of interior angles, S = (n - 2)180°, where n is the number of sides of the polygon

⇒ (n - 2)180° = 1080°
⇒ n - 2 = 6
⇒ n = 8
4. Q.  (a) What is the minimum interior angle possible for a regular polygon? Why?

 (b) What is the maximum exterior angle possible for a regular polygon?

Answer: The polygon with minimum number of sides is a triangle, and each angle of an equilateral triangle measures 60°, so 60° is the minimum value of the possible interior angle for a regular polygon. For an equilateral triangle the exterior angle is 180°-60°=120° and this is the maximum possible value of an exterior angle for a regular polygon.
The sum of the exterior angles of any polygon= 360⁰
Hence, the polygon of 8 sides is octagon.

5. Q. Find the measure of each exterior angle of a regular polygon of 9 sides.

Ans: Total measure of all exterior angles = 360

No. of sides = 9

Measure of each exterior angle = 360/9 = 40

6.Q. If the sum of the measures of the interior angles of a polygon equals the sum of the measures of the exterior angles, how many sides does the polygon have?