## Saturday, 16 February 2013

### 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?

Ans:The sum of the measures of the interior angles of a polygon with n sides =(n-2)x1800
(n-2) x1800 = 3600            Þ      n=2+2=4
7.Q. The sum of the interior angles of a regular polygon is:(n - 2) × 180° where n is the number of sides of the polygon.

Solution: The sum of its exterior angles of regular polygon= 360°
The exterior angle of a regular polygon
Interior angle of a regular polygon = sum of interior angles ÷ number of sides
8. Q.What is the measure of the each angle of regular Hexagon?

Ans: No. of sides in regular hexagon = 6
The measure of the each angle =[(2n – 4)x900 /n ]=[2x6-4]x900/6 =7200 /6 =1200
9. Q. Find the number of sides of a polygon whose each interior angle is 1560 .

Ans each exterior angle = 180 - 1560 = 240
Measure of Each Exterior Angle of a Polygon = 360/n
Þ 24= 360/n       Þ n = 360/24 =15
10.Q.  Two regular polygons are such that the ratio between their no. of sides is 1:2 and the ratio of measures of their interior angle is 3:4. Find the number of sides of each polygon.

Ans: let the number of sides are x and 2x
then their interior angles will be [{(2n-4)/n}x900]       and [{(4n-4)/n}x900]
A/Q, the ratio of measures of their interior angle = 3:4
Þ [{(2n-4)/n}x900] ¸ [{(4n-4)/n}x900] = ¾
On solving this we get , n=5
So, the numbers of sides are 5 and 2x5=10