Question

If $ABCD$ is a parallelogram then which of the following is not true?

• A. $CD=4\text{cm}\&BC=3\text{cm}$
• B. $m\angle B={60}^{\circ }$
• C. $m\angle D={120}^{\circ }$
• D. $m\angle C={60}^{\circ }$

Answer 1

The correct option is B $m\angle B={60}^{\circ }$

• As we know opposite sides of a parallelogram are equal

$\Rightarrow AB=CD=4\text{cm}\&BC=DA=3\text{cm}$

• We also know that opposite angles of a parallelogram are equal.

$\Rightarrow m\angle A=m\angle C={60}^{\circ }$

• Sum of adjacent angles of a parallelogram is ${180}^{\circ }$

$\Rightarrow m\angle A+m\angle B={180}^{\circ }\Rightarrow m\angle B={180}^{\circ }-m\angle A\Rightarrow m\angle B={180}^{\circ }-{60}^{\circ }={120}^{\circ }$

$\because m\angle B=m\angle D\Rightarrow m\angle D={120}^{\circ }$