In a quadrilateral, define the following :

$v i i i)$ Opposite angles

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Solution

Step: Define opposite angles of a quadrilateral

Two angles of a quadrilateral having no common arm are called its opposite angles.

In the given quadrilateral $A B C D, ∠ D A B, ∠ B C D; ∠ A D C, ∠ A B C,$ are the opposite angles.

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Complete each of the following, so as to make a true statement:
(i) A quadrilateral has ______sides.
(ii) A quadrilateral has ______angles.
(iii) A quadrilateral has ______vertices, no three of which are ______
(iv) A quadrilateral has ______diagonals.
(v) The number of pairs of adjacent angles of a quadrilateral is ______
(vi) The number of pairs of opposite angles of a quadrilateral is ______
(vii) The sum of the angles of a quadilateral is ______
(viii) A diagonal of a quadrilateral is a line segment that joins two ______vertices of the quadrilateral.
(ix) The sum of the angles of a quadrilateral is ______ right angles. (x) The measure of each angle of a convex quadrilateral is ______ $180 \circ$ .
(xi) In a quadrilateral the point of intersection of the diagonals lies in ______ of the quadrilateral.
(xii) A point is in the interior of a convex quadrilateral, if it is in the ______ of its two opposite angles.
(xiii) A quadrilateral is convex if for each side, the remaining ______ lie on the same side of the line containing the side.

Q. Complete each of the following, so as to make a true statement:
(i) A quadrilateral has ....... sides.
(ii) A quadrilateral has ...... angles.
(iii) A quadrilateral has ..... vertices, no three of which are .....
(iv) A quadrilateral has .... diagonals.
(v) The number of pairs of adjacent angles of a quadrilateral is .......
(vi) The number of pairs of opposite angles of a quadrilateral is .......
(vii) The sum of the angles of a quadrilateral is ......
(viii) A diagonal of a quadrilateral is a line segment that joins two ...... vertices of the quadrilateral.
(ix) The sum of the angles of a quiadrilateral is .... right angles.
(x) The measure of each angle of a convex quadrilateral is ..... 180°.
(xi) In a quadrilateral the point of intersection of the diagonals lies in .... of the quadrilateral.
(xii) A point is in the interior of a convex quadrilateral, if it is in the ..... of its two opposite angles.
(xiii) A quadrilateral is convex if for each side, the remaining .... lie on the same side of the line containing the side.

In the figure, ABCD is a quadrilateral.
(i) Name a pair of adjacent sides.
(ii) Name a pair of opposite sides.
(iii) How many pairs of adjacent sides are there?
(iv) How many pairs of opposite sides are there?

(v)Name a pair of adjacent angles.
(vi) Name a pair of opposite angles.
(vii) How many pairs of adjacent angles are there?
(viii) How many pairs of opposite angles are there?