Question

Opposite angles of a quadrilateral ABCD are equal. If AB=4cm, determine CD.

Answer 1

Hint: A quadrilateral having opposite angles equal is a parallelogram. In a parallelogram, opposite sides are equal in length. That means AB and CD will form a pair of opposite sides. If AB is equal to 4cm then CD is also equal to 4cm.

Complete step by step answer:
In the question, it is given that ABCD is quadrilateral. Let us form a quadrilateral and name the corner points A, B, C, and D respectively.

It is also given in the question that the opposite angles of the quadrilateral are equal which means $\angle A=\angle C$and $\angle B=\angle D$. If a quadrilateral has opposite angles equal then it will be a parallelogram or a rhombus. ABCD can be a parallelogram or a rhombus. We know from the property of parallelogram and rhombus that opposite angles are equal. The following figure represents a parallelogram and a rhombus.

We are given in the question that side AB is equal to 4cm. In a parallelogram, the opposite sides are equal in length. We have to determine the value of side CD, from the figure it is clear that CD is the opposite side of AB. So the value of AB will be equal the value of CD. The value of AB is 4cm, therefore the value of CD is also 4cm. Hence CD=4cm.
Note:
It should be noted that in a parallelogram opposite sides are equal in length that is AB=CD and AD=BC and opposite angles are equal that implies $\angle A=\angle C$and $\angle B=\angle D$ . And in a rhombus, all sides are equal in length that is AB=CD=AD=BC and opposite angles are equal that is$\angle A=\angle C$ and $\angle B=\angle D$ . Also make sure that the vertices of the parallelogram are taken in order A, B, C, and D while marking them in the figure.