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. ${67}^{\circ }$
• B. ${65}^{\circ }$
• C. ${80}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is D ${60}^{\circ }$

In $△ACE$,
$\angle ACE+\angle CEA+\angle EAC=180$
$20+90+\angle EAC=180$ (Sum of angles of triangle)
$\angle EAC=180-110$
$\angle EAC={70}^{\circ }$
Now, in $△ABD$,
$\angle ABD+\angle ADB+\angle BAD=180$ (Sum of angles of triangle)
$50+\angle ADB+70=180$
$\angle ADB={60}^{\circ }$