Question

In the figure, given below, CE is the perpendicular to AB, $\angle ACE={20}^{\circ }and\angle ABD={50}^{\circ }$. Find the measure of $\angle BDA$.

• A. ${36}^o$
• B. ${60}^o$
• C. ${56}^o$
• D. none of the above

Answer 1

The correct option is B ${60}^o$

In $△EAC$,
$\angle EAC+\angle AEC+\angle ACE=180$
$\angle EAC+90+20=180$
$\angle EAC=180-110$
$\angle EAC=70$
In $△ABD$
Sum of angles = 180
$\angle ABD+\angle BAD+\angle BDA=180$
$50+70+\angle BDA=180$
$\angle BDA={60}^{\circ }$