Question

Which of the following is not true for the rhombus $ABCD$ with $m\angle ABC={140}^{\circ }$ and side length of 4 cm.

• A. $AB=BC=CD=DA=4cm$
• B. $\angle A={50}^{\circ }$
• C. $\angle A+\angle B={180}^{\circ }$
• D. $\angle C+\angle D={180}^{\circ }$

Answer 1

The correct option is B $\angle A={50}^{\circ }$

All the sides of a rhombus are equal in length.
$\therefore AB=BC=CD=DA=4cm$

Also, the measures of the adjacent angles of a parallelogram add up to be ${180}^{\circ }.$
$\angle A+\angle B={180}^{\circ }$
$\Rightarrow \angle A+{140}^{\circ }={180}^{\circ }$
$\Rightarrow \angle A={180}^{\circ }-{140}^{\circ }={40}^{\circ }$

and $\angle C+\angle D={180}^{\circ }$