The sides of a quadrilateral are 3, 4, 5 and 6 cms. The sum of a pair of opposite angles is `120^0. `Show that the area of the quadrilateral is `3sqrt(30)` sq.cm.

If the sum of any pair of opposite angles of a quadrilateral is 180^@ ; then the quadrilateral is cyclic.

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

The diagonals of a quadrilateral are 16 cm and 13 cm. If they intersect each other at right angles, find the area of the quadrilateral.

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

The two adjacent sides of a cyclic quadrilateral are 2a n d5 and the angle between them is 60^0dot If the area of the quadrilateral is 4sqrt(3) , find the remaining two sides.

Three angles of a quadrilateral are in the ratio 4:6:3. If the fourth angle is 100^@ , find the ther three angles of the quadrilateral.

Three angles of a quadrilateral are in the ratio 4:6:3. If the fourth angle is 100^(@) find the three angles of the quadrilateral.

If the sides of a cyclic quadrilateral are 3,3,4,4, show that a circle be inscribed in it.

Complete each of the following, so as to make a true statement: A quadrilateral has ............ sides A quadrilateral has ............ angles. A quadrilateral has ............ vertices, no three of which are.... A quadrilateral has ............ diagonals. The number of pairs of adjacent angles of a quadrilateral is ...... The number of pairs of opposite angles of a quadrilateral is ...... The sum of the angles of quadrilateral is..... A diagonals of quadrilateral is a line segment that joins two ..... vertices of the quadrilateral. The sum of the angles of a quadrilateral is ......... right angles. The measure of each angle of a convex quadrilateral is ...... 180^0dot In a quadrilateral the point of intersection of the diagonals lie lies in .... of the quadrilateral. A point is in the interior of a convex quadrilateral, if it is in the ....... of its two opposite angles. A quadrilateral is convex if for each side, the remaining.... lie on the same side of the line containing the side.

Theorem 10.11 : The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.