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