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The circle below has center C suppose

The circle below has center C suppose-example-1
User Nikmin
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Applying the inscribed angle theorem, we have: m(ED) = 112° and m∠ECD = 112°.

How to apply the inscribed angle theorem?

Recall that the in a circle where we have an inscribed angle that is subtended by an arc, the measure of the inscribed angle is always half of the measure of the subtended arc, while the subtended arc's measure is equal to he measure of the central angle.

Angle DEF is an inscribed angle that measures 56 degrees, angle ECD is a central angle, and arc ED is the subtended arc, therefore:

m(ED) = 2(m∠DEF)

Substitute:

m(ED) = 2(56)

m(ED) = 112°

m∠ECD = m(ED)

m∠ECD = 112°

User Sushil Pandey
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