Radians: Points A, B, C and D divide circumference of circle in the ratio 1:2:3:4...

kiu1

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Question: Points A, B, C and D divide the circumference of a circle in the ratio 1:2:3:4. Find the angles of the cyclic quadrilateral ABCD in radians.
The answers are 3pi/10, pi/2, 7pi/10 and pi/2.

But I don't really understand because what I calculated are 36, 72, 108, 144 degrees respectively. [using 360/(1+2+3+4) and multiply the ratio]. How can I get the above answer?? Thanks
 
You have done well to use Central Angles to solve the first part.

Now, draw the rectangle and switch your thinking to Inscribed Angles.

Hint: Each Inscribed Angle contains two of your circumference pieces.

Let's see what you get!
 
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