Question

In circle A below, chord BC and diameter DAE intersect at F. If mCD= 46° and mDB= 102° , what is ∠CFE?

(Pls help me i need this turned in tonight and this is the last question on my assignment)

Answer 1

∠CFE = 118°

Explanation:

You want the measure of angle CFE given arcs CD = 46° and DB = 102°, where DE is a diameter of circle A.

Arc CE

The measure of arc CE is the supplement of arc CD, so is ...

arc CE = 180° -45° = 134°

Angle CFE

The measure of angle CFE is the average of the measures of the arcs the chords subtend:

(DB +CE)/2 = (102° +134°)/2 = 118°

The measure of angle CFE is 118°.

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Additional comment

The figure in the attachment is drawn to scale.

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