Question

The acute angle made by the sides of the parallelogram is:

• A. ${60}^{\circ }$
• B. ${55}^{\circ }$
• C. ${50}^{\circ }$
• D. ${45}^{\circ }$

Answer 1

The correct option is B ${55}^{\circ }$

$\Rightarrow$ Let $ABCD$ be the parallelogram which we have to construct.

$\Rightarrow$ $AC=5cm$ and $BD=9cm$ and angle between them i.e. $\angle AOD$ and $\angle COB$ is ${60}^{\circ }$.

$\Rightarrow$ Draw a line segment $AC=5cm$.

$\Rightarrow$ Draw a midpoint $O$ on $AC$.

$\Rightarrow$ Construct an angles of ${60}^{\circ }$ at point $O$ with respect to $A$ and $C$.

$\Rightarrow$ Take $O$ as a center with radius $4.5cm$ cut off $OD$ and $OB$.

$\Rightarrow$ Join $AD,AB,BC$ and $CD$.

$\Rightarrow$ Thus, parallelogram $ABCD$ is required parallelogram.

$\Rightarrow$ We have to measure acute angle made by sides which is $\angle ADC$ and $\angle ABC$.

$\therefore$ $\angle ADC=\angle ABC={55}^{\circ }$