Question

ABC is a cyclic quadrilateral whose diagonals intersect at point E. If DBC=70°, BAC is 30° find BCD. Further if AB=BC.Find ECD

Answer 1

Step-by-step explanation:

As angle BAC is 30°, angles BAC and BDC will be 30° by a property which says angles in the same segment are equal. Now in triangle BDC ,70°+30°+angle BCD = 180° by angle sum prop.

Therefore ,we will get angle BCDas 80°.

Now if AB=BC ,in triangle ABC angle BAC=BCA as angles opp. to equal sides are equal. therefore we will get angle BAC =BCA=30° .

but we have angle BCD as 80° ,ECD will be BCD-BCA ,which will be ECD=80°-30° which is 50°