If the measure of arc DEF is 232�, what is the measure of ∠DEF?
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OpenStudy (anonymous):
OpenStudy (lukebluefive):
Aren't those the same thing?
OpenStudy (anonymous):
that's what they gave me
OpenStudy (lukebluefive):
They may have meant that the measure of arc DAF is 232. Since it's a central angle (focused on the midpoint of a circle), it is twice the measure of the inscribed angle DEF (made by any three points on a circle). That means that angle DEF = angle DAF / 2.
OpenStudy (anonymous):
so 232 times 2
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OpenStudy (lukebluefive):
232 / 2
OpenStudy (lukebluefive):
I think they made a typo. DEF isn't an arc, it's an angle. Arcs only exist in the middle of a circle. Angles are made when two lines intersect. The only arc that could exist in that figure with the endpoints "D" and "F" is arc DAF.
OpenStudy (anonymous):
i know i may seem like a blonde right now but my brain is tired is it dividing then
OpenStudy (lukebluefive):
Everyone has blonde moments. Yes, just divide 232 by 2.
OpenStudy (lukebluefive):
I'm fairly certain that's the correct answer.
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OpenStudy (anonymous):
thanks i owe you big time you are my lifesaver :) <3
OpenStudy (lukebluefive):
No problem. The wording of the problems is making them seem way harder than they actually are.