Question

Let ABC be a triangle with AB = AC and D be a point on BC such that \( \angle BAD = 30^\circ \). If E is a point on AC such that AD = AE, then \( \angle CDE \) equals:

• A. \(15^\circ\)
• B. \(60^\circ\)
• C. \(30^\circ\)
• D. \(10^\circ\)

Hint:

In geometry problems involving isosceles triangles and angles, use symmetry and angle sum properties to simplify calculations and derive unknown angles.

Answer 1

The Correct Option is A

Since AB = AC and \( \angle BAD = 30^\circ \), triangle ABD is isosceles. Thus, \( \angle ABD = \angle ADB = 30^\circ \). Step 2: Now, since AD = AE, triangle ADE is also isosceles, and \( \angle ADE = \angle DEA \). Step 3: Considering the angle properties and the geometry, we conclude: \[ \angle CDE = 15^\circ. \]