Regular polygon has all sides equal in length and all angles equal in size.
The sum of interior angles of n sided polygon is
s = (n - 2) x 180°
Problem 1 :
Each interior angle of a regular polygon is 174⁰. Find the number of sides of polygon.
Solution :
So, the number of sides of polygon is 6. Then the polygon is known as hexagon.
Problem 2 :
The interior angle of a regular polygon is 135⁰. Work out the number of sides of the polygon.
Solution :
So, the number of sides of the regular polygon is 8.
Problem 3 :
The sum of the interior angles in a polygon is 7380⁰. Calculate the number of sides the polygon has.
Solution :
Sum of the interior angles of a polygon = (n - 2) x 180
(n - 2) x 180 = 7380
n - 2 = 7380/180
n - 2 = 41
Add 2 on both sides, we get
n = 41 + 2
n = 43
Problem 4 :
Shown below is a regular pentagon ABCDE
Solution :
Number of sides of given polygon = 5
Sum of interior angles = (n - 2) x 180
= (5 - 2) x 180
= 3 x 180
= 540
Measure of each angle = 540/5
x = 108
In triangle BDC,
DC = BC
∠BDC + ∠DCB + ∠CBD = 180
∠BDC = ∠CBD
y + x + y = 180
2y + x = 180
2y + 108 = 180
2y = 180 - 108
2y = 72
Dividing by 2 on both sides.
y = 72/2
y = 36
Problem 5 :
Shown below is a regular hexagon, with an exterior angle labeled y.
Work out the size of each exterior angle.
Solution :
Number of sides of the polygon above = 6
Sum of the angles of the polygon = (6 - 2) x 180
= 4(180)
= 720
Measure of each angle = 720/6
= 120
Sum of interior angle + y = 180
120 + y = 180
y = 180 - 120
y = 60
Problem 6 :
Shown is a regular hexagon and a regular octagon.
Solution :
Number of sides of hexagon = 6
Number of sides of octagon = 8
y = 360 - (120 + 135)
y = 360 - 255
y = 105
Problem 7 :
Shown below is a regular hexagon ABCDEF.
Calculate the angle x.
Solution :
Measure of each angle of hexagon = 120
Since it is regular polygon, CD = BC
∠CDB + ∠CBD + ∠BCD = 180
x + x + 120 = 180
2x + 120 = 180
Subtracting 120 on both sides.
2x = 180 - 120
2x = 60
Dividing by 2, we get
x = 60/2
x = 30
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM