Test: Polygons - Class 8 MCQ

Circle is an example of a 2-D geometrical shape that is not a polygon.

The two examples of a convex polygon are Pentagon and Hexagon.

No. of diagonals in a polygon of n sides = n (n – 3 ) / 2

14 = n (n – 3) / 2

14 × 2 = n ( n – 3)

28 = n ( n – 3)

28 = 7 (7 -3)

Therefore n = 7

We know that sum of all the interior angles in a polygon = (n – 2) × 180°

Here, n = 13

Therefore, the sum of all interior angles = (13 – 2) × 180°

= 11 × 180°

= 1980°

The formula of sum of all the interior angles of a polygon is = (n – 2) × 180°

Given, the sum of interior angles of the given polygon is 1440

(n – 2) × 180 = 1440

n – 2 = 1440 / 180

n – 2 = 144 / 18 = 8

n – 2 = 8

n = 10

Exterior angle = 360 / n

Given n = 6

Exterior angle = 360 / 6 = 60.

To calculate the number of sides of a polygon,

Number of sides = ½ [( sum of interior angles / 90) + 4 ]

= ½ ( (9 × 90) / 90 + 4)

= ½ ( 9 + 4)

= ½ ( 13 )

= 6.5

No it is not possible to have a polygon where the sum of whose interior angles is 9 right angles, since we got the number of sides as 6.5.

We know that

Number of sides = ½ ( sum of interior angles / 90 + 4 )

n = ½ ( 910°/90° + 4)

n = ½ (10.11 + 4 )

Since n is not a positive integer/whole number, (the value of n is in decimals), there cannot be a polygon whose interior angle is 910°.

Number of sides given is 9

Formula for each interior angle is ((2n – 4) × 90) / n

= [(2 × 9 – 4) × 90] / 9

= (14 × 90) / 9

= 1260 / 9

= 140°

We know that

Interior angle + Exterior angle = 180 degrees

If Interior angle = Exterior angle

Then Exterior angle + Exterior angle = 180 degrees

2 Exterior angle = 180 degrees

Exterior angle = 180 / 2

Exterior angle = 90.

But Interior angle = Exterior angle = 90 deg

Number of sides n = 360/(180 – interior angle)

n = 360 /( 180 – 90)

n = 360 / 90

n = 4.

A polygon with 4 sides has both interior angles and exterior angles as same.