Look at quadrilateral LMJK in the circle shown below.

Based on this figure which statement proves that the opposite angles of an inscribed quadrilateral are supplementary?
Answer

a = 2 × angle KJM, b = 2 × angle KLM, and a + b = 360°.
a = 2 × angle KLM, b = 2 × angle KJM, and a + b = 360°.
Angle KJM is a, angle KLM is b, and a + b + angle JKL + angle LMJ = 360°.
Angle KLM is a, angle KJM is b, and a + b + angle JKL + angle LMJ = 360°.

Question

Look at quadrilateral LMJK in the circle shown below. 



Based on this figure which statement proves that the opposite angles of an inscribed quadrilateral are supplementary? 
Answer 

a = 2 × angle KJM, b = 2 × angle KLM, and a + b = 360°.
a = 2 × angle KLM, b = 2 × angle KJM, and a + b = 360°.
Angle KJM is a, angle KLM is b, and a + b + angle JKL + angle LMJ = 360°.
Angle KLM is a, angle KJM is b, and a + b + angle JKL + angle LMJ = 360°.

anonymous · Answer

attachment

anonymous · Answer

@matt101 Could you look at this too? This is the last one.

matt101 · Answer

It has to be one of the first two since a and b alone must equal 360. I'm inclined to go with the first answer by following a similar logic to the other question with the circle, but it would be great if someone else could confirm.

mertsj · Answer

Same as before.  Angle J and angle a have the same arc but a is a central angle and J is inscribed so a is twice J.  Similarly b is twice L.  Or we could say that J is (1/2)a and L is (1/2)b|dw:1338863084011:dw|