Question

AB $\perp$ BC, BD $\perp$ AC and CE bisects $\angle C$, $\angle A = 30^\circ$. Then what is $\angle CED$?

• A. $30^\circ$
• B. $60^\circ$
• C. $45^\circ$
• D. $65^\circ$

Hint:

When angle bisectors appear in right triangles, break the larger triangle into smaller ones and use the angle sum property carefully.

Answer 1

The Correct Option is B

Step 1: Understanding the diagram In $\triangle ABC$, AB $\perp$ BC and $\angle A = 30^\circ$. So $\triangle ABC$ is right-angled at (b) 

Step 2: Finding $\angle C$ Sum of angles in $\triangle ABC$: $\angle C = 180^\circ - 90^\circ - 30^\circ = 60^\circ$. 

Step 3: Role of CE bisector CE is the angle bisector of $\angle C$, so $\angle ECD = \angle ECA = 30^\circ$. 

Step 4: $\triangle CED$ analysis In right triangle $\triangle CED$, using geometry properties (and symmetry from perpendicular BD), $\angle CED$ = $60^\circ$.