Question

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.

Answer 1

Angle C would equal 59 degrees

Answer 2

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.