Question

In the given fig., ∆ABC is an isosceles with AB= AC and ∠ ABC =

50° . Find ∠ BDC and ∠ BEC.​

Answer 1

ANSWER =angle BDC = 80° and angle BEC = 100°

FULL explanation=In ∆ABC, we have,

AB = AC

=> angle ACB = angle ABC

=> angle ACB = 50° (since, angle ABC = 50°)

Therefore,

angle BAC = 180° - (angle ABC + angle ACB)

=> angle BAC = 180° - (50° + 50° ) = 80°

Now,

Since angle BAC and angle BDC are angles in the same segment.

Therefore,

angle BDC = angle BAC

=> angle BDC = 80°

Now,

BDCE is a cyclic quadrilateral.

Therefore,  

angle BDC + angle BEC = 180°

=> 80° + angle BEC = 180°

=> angle BEC = 100°

Hence,

angle BDC = 80° and angle BEC = 100°

Answer 2

BDC=80

BEC=100

HOPE IT HELPS