Question

Consider quadrilateral BCEF inscribed in circle A. Diagonals EB and CF intersect at point D. Select all the statements that are true about the diagram above

Answer 1

`m\angle ECB+m\angle EFB=180`

`m\angle CDB\cong m\angle EDF`

`m\angle CDB+m\angle DCB+m\angle CBD=180 \degree`

Explanation:

From the diagram, quadrilateral BCEF is a cyclic quadrilateral.

Opposite angles if a cyclic quadrilateral sum up to 180°

`m\angle ECB+m\angle EFB=180`

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

`m\angle CDB\cong m\angle EDF`

Also sum of angles in triangle CBD is 180°.

`m\angle CDB+m\angle DCB+m\angle CBD=180 \degree`