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°
Sum of exterior angles of any polygon is 360 degree.
Find the indicated angle measures, x.
Problem 1 :
Solution :
The sum of the exterior angle of polygon = (n - 2) × 180°
= (5 - 2) × 180°
= 3 × 180°
= 540°
∠P + ∠A + ∠E + ∠N + ∠T = 540°
115° + 85° + 97° + 125° + x° = 540°
422° + x° = 540°
x° = 540 - 422
x° = 118
Problem 2 :
Solution :
The sum of the exterior angle of polygon = (n - 2) × 180°
= (6 - 2) × 180°
= 4 × 180°
= 720°
∠A + ∠B + ∠C + ∠D + ∠E + ∠F = 720°
x° + 107° + 98° + 140° + 107° + 143° = 720°
595° + x° = 720°
x° = 720 - 595
x° = 125
Problem 3 :
Solution :
The sum of the exterior angle of polygon = (n - 2) × 180°
= (4 - 2) × 180°
= 2 × 180°
= 360°
∠BAD = 180° - 103°
∠BAD = 77°
∠BAD + ∠D + ∠B + ∠C = 360°
77° + 67° + 57° + x° = 360°
201° + x = 360°
x° = 360 - 201
x° = 159
Problem 4 :
An exterior angle and the interior angle of a regular polygon are in the ratio 2:7. Find the number of sides of the polygon.
Solution :
Let x be the interior angle, then 180-x be the exterior angle.
(180-x) : x = 2 : 7
(180-x)/x = 2 / 7
2x = 7(180-x)
2x = 1260 - 7x
2x + 7x = 1260
9x = 1260
x = 1260/9
x = 40
Exterior angle is 40 degree. Interior angle = 140
Hence, the number of sides in the polygon is 9.
Problem 5 :
Find the number of sides of a regular polygon whose each exterior angle measures 60°.
Solution :
Sum of all exterior angles = 360°
n × 60 = 360
n = 360/60
n = 6
Hence, the number of sides in the polygon is 6.
Find x in :
Problem 6 :
Solution :
The sum of the exterior angle of any polygon is 360°.
118° + 100° + x° = 360°
218° + x° = 360°
x° = 360 - 218
x° = 142
Problem 7 :
Solution :
The sum of the exterior angle of any polygon is 360°.
87° + 71° + 90° + x° = 360°
248° + x° = 360°
x° = 360 - 248
x° = 112
Problem 8 :
Solution :
The sum of the exterior angle of any polygon is 360°.
96° + 90° + x° + x° + x° = 360°
186° + 3x° = 360°
3x° = 360° - 186°
3x° = 174
x° = 174/3
x° = 58
May 21, 24 08:51 PM
May 21, 24 08:51 AM
May 20, 24 10:45 PM