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If m arc CD = 143°, and m arc AB = 39°, what is m∠ DEC ?

User Quintin B
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1 Answer

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Answer:


m\angle DEC=91^o

Explanation:

see the attached figure to better understand the problem

we know that

The measure of the interior angle is the semi-sum of the arcs comprising it and its opposite

so


m\angle DEC=(1)/(2)[arc\ AB+arc\ DC]

substitute the given values


m\angle DEC=(1)/(2)[39^o+143^o]


m\angle DEC=(1)/(2)[182^o]


m\angle DEC=91^o

If m arc CD = 143°, and m arc AB = 39°, what is m∠ DEC ?-example-1
User Jklaus
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