Question

Consider the quadrilateral BCEF inscribed in circle A. Diagonals EB and CF intersect at point D.

Answer 1

Quadrilateral BCEF in circle A with diagonals EB and CF is given below.

Step-by-step explanation:

From the diagram, quadrilateral BCEF is a cyclic quadrilateral.

Opposite angles if a cyclic quadrilateral sum up to 180°

m∠ECB + m∠EFB=180

The diagonals intersect at D to form two pairs of vertical angles, and vertical angles are congruent

m∠CDB≅m∠EDF

Also sum of angles in triangle CBD is 180°.

m∠CDB +m∠DCB+m∠CBD =180