in the diagram below chords AB and CD intersects at E. If mAC=72 and mAEC=58. how many degrees are in mDB?
1 answer:
Answer:
44°
Step-by-step explanation:
∠ DEB and ∠ AEC are vertical and congruent
Thus ∠ DEB = 58°
The measure of the chord- chord angle DEB is half the sum of the measures of the arcs intersected by the angle and its vertical angle, that is
(DB + AC ) = 58° ( multiply both sides by 2 )
DB + AC = 116°, that is
DB + 72° = 116° ( subtract 72° from both sides )
DB = 44°
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