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

Answer:

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

$m\angle CDB\cong m\angle EDF$

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

Step-by-step 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°.

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