PLEASE EXPLAIN THIS ALSO, REALLY APPRECIATE IT.

Question

In ⊙L, what is?

1. A.
2. 62
3. 
   
4. B.
5. 67
6. 
   
7. C.
8. 70
9. 
   
10. D.
11. 73

Answer 1

The measure of angle Q = 1/2 the measure of its intercepted arc so:

m<Q = 1/2 arc MNP

since arc MNP = arc MN + arc NP

m<Q = 1/2 (arc MN + arc NP)

since arc MN = 84 and m<Q = 73

73 = 1/2 (84 + arc NP)

146 = 84 + arc NP

62 = arc NP (A)

Answer 2

There is a very useful theorem, Mark M terms it inscribed angle, I call it cord theorem

Draw a cord MP, the theorem says the central angle from center facing the cord is twice that of

the angle made by picking a point opposite on the circle facing the cord.

that is, angle MLP is 146 degrees and so is measure of arc MP