Find the Angle in this Cyclic Quadrilateral | Fast & Easy Tutorial

[easy_s]

i didn't know about the angle=arc/2 rule (I always thought arc length=angle x radius) so what I did is draw a couple of lines from the centre of the circle. One line perpendicular to AB and another perpendicular to BC.
The line perpendicular to AB cuts arc AB in half to two parts of 18x and the line perpendicular to BC cuts arc BC in half to two parts of 12x-1.
The angle between these two lines then is 18x+12x-1=30x-1. Angle B then is 180-(30x-1)=181-30x. And since angle D=28x+5 that gives 180=181-30x+28x+5 which gives 2x=6 and so x=3. Angle B then is 181-30x=181-90=91.

[Footballfan-rjgf]

At first everyone will think it's very diffucult, but if you know theory and can put this in practice, so you can solve it very easily.

[geoffreyparfitt]

How can there be such a connection between angle and arc length? If the size of the circle changed, the arc length would change but the angle would not. Also, if x = 3 then the arc length is 178. What are the units? Metres?

[douglasfeather]

I'm sorry there are 2 glaring errors in this. Firstly you say that Angle = (1/2) * Arc. This is true if the radius of the circle is 1 and the Angle is measured in radians. So the two errors are 1. the original problem needs to state the radius of the circle, 2. you can't just switch from a value being measured in radians to then saying it has the same value measured in degrees. Actually if the radius of the circle is 180/PI units and you put in the correct factors of the radius of the circle and the switch from radians to degrees these factors would cancel out and your answer would be correct.