Which of the following is/are not the interior angle(s) o...
Which of the following is/are not the interior angle(s) of a regular polygon?
I.108°
II. 116°
III. 120°
I only
II only
III only
I and III only
Correct answer is B
Using the formula, (n - 2) \times 180° to get the sum of the interior angles. Then we can have
(n - 2) \times 180° = 108n ... (1)
(n - 2) \times 180° = 116n ... (2)
(n - 2) \times 180° = 120n ... (3)
Solving the above given equations, where n is not a positive integer then that angle is not the interior for a regular polygon.
(1): 180n - 360 = 108n \implies 72n = 360
n = 5 (regular pentagon)
(2): 180n - 360 = 116n \implies 64n = 360
n = 5.625
(3): 180n - 360 = 120n \implies 60n = 360
n = 6 (regular hexagon)
Hence, 116° is not an angle of a regular polygon.
In how many ways can 6 coloured chalks be arranged if 2 are the same colour? ...
The length of a rectangle is 10 cm. If its perimeter is 28 cm, find the area ...
If y = x2 - 2x - 3, Find the least value of y and corresponding value of x...
The height of a cylinder is equal to its radius. If the volume is 0.216 \pi m^3. Calculate t...
Make T the subject of the relation. ...
If X = {all the perfect squares less than 40} Y = {all the odd numbers fro, 1 to 15}. Find X ∩ ...