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Opposite angles of quadrilateral $ABCD$ are equal. If $AB = 4cm$, determine $CD$.
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A) $3$cm
B) $4$cm
C) $5$cm
D) $6$cm

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Last updated date: 28th Feb 2024
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IVSAT 2024
Answer
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Hint: We are given a quadrilateral and also we are being mentioned that the opposite angles of quadrilateral are equal we have to find the length of one side as a length of one side is already given for this first we should know that if the opposite angles of a quadrilateral is equal then it must be a parallelogram.
A quadrilateral is a parallelogram if it’s opposite angles are equal or its opposite sides are equal or one pair of opposite sides are equal and parallel.
So by using this property we will find the sides of the quadrilateral given.

Complete step-by-step solution:
Step1: We are given a quadrilateral $ABCD$ in which $AB = 4cm$ and opp-
Site angles are given equal for this first we will draw a quadrilateral from
The figure it can be seen that $AB$ and $CD$ are the opposite sides.
Step2: As we know that the quadrilateral having opposite sides will
 be a parallelogram because it is a property of quadrilateral that if its opposite angles are equal or its types are equal then it must be a parallelogram
As opposite angles are equal than opposite sides must also be equal. Using this property as $AB$ and $CD$ are the opposite sides. We can say $AB = CD$. Substituting the value of $AB$ we get
$CD = 4$cm.

Hence option (B) is the correct answer.

Note: In such types of questions students should remember the Properties of Quadrilaterals and various types of quadrilaterals. If know their property then by one specification they can easily find the type of quadrilateral on which question is based and then we can solve the further question based on the properties of that particular quadrilateral these questions are based on property don't require calculation just apply the property correctly