Question

In a quadrilateral $ABCD$, $\angle A+\angle D={180}^{\circ }$. Does this mean $AB||DC$? Why? What special name does this quadrilateral have?

Answer 1

Since $ABCD$ is a quadrilateral and,

$\angle A+\angle D={180}^{\circ }$

From the figure, we can see that $\angle A$ and $\angle D$ from the adjacent angle pair, and it is already known that the two adjacent angles always add to give their sum equal to ${180}^{\circ }.$

Also, adjacent angles are formed if the two lines are parallel which means that if two adjacent angles are given then the two lines must be parallel therefore $AB\parallel CD.$

If the two lines are parallel and also, the angle sum of two adjacent angles equal to ${180}^{\circ }$, then this type of quadrilateral is known as trapezium.