Question

In the figure above, ABCD is a cyclic quadrilateral. What ja the value of x in degrees?

Answer 1

Explanation:

Remark

The diagram makes the line AB look like it is tilted a bit to the right. I'm going to assume that isn't right. AB extended is a straight line. ADC is supplementary to the 80o angle.

Solution

<ADC + 80o = 180 They are on the same straight line

<ADC = 180 - 80 Subtract 80 from both sides

<ADC = 100o

Opposite angles of a cyclic quadrilatral are supplementary

<ADC + <ABC = 180 Property of cyclic quadrilaterals

100 + <ABC = 180 Subtract 100 from both sides

<ABC = 80 degrees.

<x + <ABC = 180

<x + 80 = 180

<x = 100 degrees

Discussion

I cannot be sure what the arc at B is equal to. Is the arc = 80 o or is <ABC = 80. And it is unresolvable. My suggestion is that you ask your teacher.