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Quadrilateral ABCD is inscribed in circle O.

What is m∠C?

Enter your answer in the box.


____°


Please show how to solve this question. Thanks again.

Quadrilateral ABCD is inscribed in circle O. What is m∠C? Enter your answer in the-example-1

2 Answers

5 votes
Angle C would equal 59 degrees
User Nurettin
by
7.6k points
3 votes

To solve this question we will have to make use of one of the properties of the inscribed quadrilateral. That property is: "Opposite angles in any quadrilateral inscribed in a circle are supplements of each other".

Thus, as we can see from the diagram given,
\angle B+\angle D=180^(\circ)


(2x+3)+(4x+3)=180^(\circ)


\therefore 6x+6=180^(\circ)


6x=174^(\circ)


\therefore x=(174^(\circ))/(6) =28^(\circ)

Thus, now that we know the value of x, we can easily find the value of the
\angle C because we know that:


\angle C=2x+1


\therefore \angle C=2(29^(\circ))+1=59^(\circ)

Thus,
\boldsymbol{59^(\circ)} is the correct answer.


User Satishakumar Awati
by
8.0k points
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