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

The sum of either pair of opposite angles of a cyclic quadrilateral is 180^0 OR The opposite angles of a cyclic quadrilateral are supplementary.

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.

Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^@

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

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 two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

If the two sides of a pair of opposite sides of a cyclic quadrilateral are equal, prove that its diagonals are equal.

Theorem 8.3 : If each pair of opposite sides of a quadrilateral is equal, then it is a parallelogram.

If the sum of the two angles of a quadrilateral is 180^0dot What is the sum of the remaining two angles?