Question

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If ∠DBC = 70°, ∠BAC is = 30°, find ∠BCD. Further, ifAB = BC, find ∠ECD.

Answer 1

Answer:

angle BCD = 80 and angle ECD = 50

Step-by-step explanation:

angle DBC = angle DAC (angles subtended on the same arc touching the circumference of a circle are equal)

so, angle DAC = 70

now,  angle DAB = angle BAC + angle DAC

                            = 70 + 30

                            = 100

angle BCD = 180 - angle DAB (opposite angles of a cyclic quadrilateral are supplementary)

angle BCD = 180 - 100

                  = 80

if AB = BC

so, triangle ABC is an isosceles triangle.

so, angle BAC = angle BCA

angle BCA = 30

and, angle ECD = angle BCD - amgle BCA

                          = 80 - 30

                           = 50

Hope this helps, please mark brainliest.