Question

The isosceles right angled triangle $ABC$ and square $ACDE$ share side $AC$ as shown in the above figue. Find the degree measure of angle $EBC$.

• A. $27$
• B. $30$
• C. $60$
• D. $63$
• E. $75$

Answer 1

The correct option is A $27$

In given figure, $ACDE$ is square and $ABC$ is the isosceles right angled triangle.

Then $AC=AE=CD=ED=BC$

Then $BD=BC+CD$

Then $\tan EBD=\frac{ED}{BD}$

$\Rightarrow \tan EBD=\frac{ED}{2ED}$

$\Rightarrow \tan EBC=0.50$

But value of $\tan 27=0.50$

Then $\angle EBC=27$