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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

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 class=

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Answer:

[tex]m\angle ECB+m\angle EFB=180[/tex]

[tex]m\angle CDB\cong m\angle EDF[/tex]

[tex]m\angle CDB+m\angle DCB+m\angle CBD=180 \degree[/tex]

Step-by-step explanation:

From the diagram, quadrilateral BCEF is a cyclic quadrilateral.

Opposite angles if a cyclic quadrilateral sum up to 180°

[tex]m\angle ECB+m\angle EFB=180[/tex]

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

[tex]m\angle CDB\cong m\angle EDF[/tex]

Also sum of angles in triangle CBD is 180°.

[tex]m\angle CDB+m\angle DCB+m\angle CBD=180 \degree[/tex]