In the figure ,chord AB and CD intersect at E.If ZBED-95°, m(arc BD)=100°, find m(arc AC)
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Step-by-step explanation: We know, if two chords of a circle intersect each other in the interior of a circle, then the measure of the angle between them is half the sum of measures of the arcs intercepted by the angle and its opposite angle.
∴∠ABE=
2
1
[m(arcAE)+m(arcDC)]
⇒m(arcAE)+m(arcDC)=2∠ABE
⇒95
o
+m(arcDC)=2x108
o
⇒m(arcDC)=216
o
—95
o
=121
o
Thus, the measure of arc DC is 121
o
.
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