Question

Find angle boc and bdc

Answer 1

angle ABC = angle ACB [ angles opposite to equal sides of a triangle are equal ]

In ∆ABC,

angle ABC + angle ACB + angle BAC = 180° [ sum of all interior angles of a triangle is 180° ]

50° + 50° + angle BAC = 180°

angle BAC = 80°

Now,

angle BAC = (1/2) angle BOC [ angle formed by a segment at the centre is double the angle formed on anywhere on the circle ]

angle BOC = 2 × 80

angle BOC = 160°

Since ABDC is a cyclic quadrilateral because all vertices are on the circle , THEREFORE,

angle BDC + angle BAC = 180° [ sum of opposite angles of a cyclic quadrilateral is 180° ]

angle BDC + 80° = 180°

angle BDC = 100°