Question

In the figure, ABCD is a quadrilateral. Name the pairs of opposite angles.

Answer 1

Hint: In geometry, a Quadrilateral can be defined as a closed, two-dimensional shape which has four sides. Two angles of a quadrilateral are said to be opposite angles of the quadrilateral, if they are not adjacent. So from the figure we have to check for two angles which are not adjacent to it.
 
Complete step-by-step answer:
Two sides of a quadrilateral are said to be adjacent sides of the quadrilateral, if they have a common endpoint.

From the figure, (AB,BC), (BC,CD), (AB,AD) are the pair of adjacent sides of the quadrilateral. 
Two sides of a quadrilateral are said to be opposite sides of the quadrilateral, if they are not adjacent.
From the figure, (AB,DC) and (BC,AD) are the pair of opposite sides of the quadrilateral
Two angles of a quadrilateral are said to be adjacent angles of the quadrilateral, if they have a side of the quadrilateral in common.
\[(\angle A,\angle B), \, (\angle B,\angle C),\, (\angle C,\angle D),\, (\angle D,\angle A)\] are the pair of adjacent angles of quadrilateral.
Two angles of a quadrilateral are said to be opposite angles of the quadrilateral, if they are not adjacent.
\[(\angle A,\angle C),\, (\angle B,\angle D)\] are the pair of opposite angles of quadrilateral.

Hence \[(\angle A,\angle C),\,(\angle B,\angle D)\] are the pair of opposite angles of quadrilateral.

Note:
Properties of a Quadrilateral:
1) A quadrilateral has 4 sides, 4 angles and 4 vertices.
2) A quadrilateral can be regular or irregular.
3) The sum of all the interior angles of a quadrilateral is 360°.
Quadrilaterals can be classified into Parallelograms, Squares, Rectangles and Rhombuses. Square, Rectangle and Rhombus are also Parallelograms.
Different quadrilateral has a different property for its opposite angles:

Name of Quadrilateral	Description
Parallelogram	2 pairs of parallel sides. Opposite sides and opposite angles are congruent.
Rectangle	2 pairs of parallel sides. 4 right angles (90°). Opposite sides are parallel and congruent. All angles are congruent.
Square	4 congruent sides. 4 right angles (90°). Opposite sides are parallel. All angles are congruent.
Rhombus	Opposite angles are equal
Trapezoid	Only one pair of opposite sides is parallel.