YatesDevon9662 YatesDevon9662
  • 02-01-2020
  • Mathematics
contestada

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

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calculista
calculista calculista
  • 08-01-2020

Answer:

[tex]m\angle DEC=91^o[/tex]

Step-by-step 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

[tex]m\angle DEC=\frac{1}{2}[arc\ AB+arc\ DC][/tex]

substitute the given values

[tex]m\angle DEC=\frac{1}{2}[39^o+143^o][/tex]

[tex]m\angle DEC=\frac{1}{2}[182^o][/tex]

[tex]m\angle DEC=91^o[/tex]

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