Question

In the given figure, ABCD is a parallelogram, $\angle ADE={50}^{\circ }$ and $\angle ACE=\angle BED={90}^{\circ }$. The value of $\angle EAC+\angle ABC-2\angle DAC$ is

• A. ${20}^{\circ }$
• B. ${10}^{\circ }$
• C. ${30}^{\circ }$
• D. ${40}^{\circ }$

Answer 1

The correct option is B ${10}^{\circ }$

From given, we have,

$\angle BED={90}^{\circ }$

And $\angle AEC={45}^{\circ }$

Then the $\angle EAB={45}^{\circ }$

$\angle ABC$ is equal to ${45}^{\circ }$

$\angle ADE={50}^{\circ }$

And $\angle DAC={40}^{\circ }$

$\angle EAC+\angle ABC-2\angle DAC={45}^{\circ }+{45}^{\circ }-2\times {40}^{\circ }$

$={90}^{\circ }-{80}^{\circ }$

$={10}^{\circ }$