EXERCISE 19 E

1.Find the number of sides of a regular polygon in which each interior angle is 162°.

2.How many sides has a polygon the sum of whose interior angles is 1980deg ?

3.The angles of a quadrilateral taken in order are 2x , 3x , 7x ,8x. Find x and prove that two opposite sides are parallel.

4.ABCDE is a regular pentagon. AB. DC are produced to meet at P. Find angleBPC.

5.Find the sum of the interior angles of a polygon which has (i) 30 sides. (ii) 40 sides.

6.Prove that the sum of the interior angles of an octagon is twice the sum of the interior angles of a pentagon

7.In a regular pentagon ABCDE, calculate the number of degrees in the angle ABC and prove that BC||AD

8.(i) Is it possible to draw a regular polygon with exterior angles

(a) 72 deg (b) 32 deg (c) 40 deg (d) 55 deg (e) 60 deg ? Where possible give the number of sides

(ii)Is it possible to draw a regular polygon with interior angles

(a) 120 deg (b) 156 deg (c) 145 deg ? Where possible , state the number of sides.

9.The number of sides of two regular polygons are in the ratio of 3:2 and their interior angles are in the ratio 5:3 . Find the number of their sides.

10.The sides of a pentagon are produced in order and the exterior angles so obtained measure 2x+20 deg , x-10 deg , 3x+30 deg , 4x-15 deg , 5x-10 deg . Find the measure of x and find all the exterior angles of the pentagon.

11.The ratio between the interior and exterior angles of a regular polygon is 8:1. Find

(i) The number of sides of the regular polygon

(ii) each exterior angle of the polygon

12.An octagon has two pairs of equal angles , one measuring 72 deg and the other 56 deg and 4 equal angles . Find the size of equal angles.

13.Each exterior angle of a regular polygon is two-thirds of its interior angle. Find the number of sides in the regular polygon

14.Each interior angle of a regular polygon is 160 deg . Find the interior angle of regular polygon which has double the number of sides as the given polygon.

15.Two interior angles of a polygon are right angles and sum of remaining angles is 420 deg. Find the number of sides of the polygon.