Determine the measure of ∠nop.
a) 15°
b) 20°
c) 40°
d) 50°

The correct option is B.

Step-by-step explanation:

Let the center of the circle is E, and the line ON intersect the circle at A and D. The line OP intersect the circle at B and C.

Let the measure of ∠NOP be x.

Draw line segments AC, BD, AE, BE, CE and DE.

According to the central angle theorem, the angle inscribed on the circle from the angle two point on the circle is half of its central angle.

By using central angle theorem,

According to the exterior angle theorem, the sum of two interior angles of a triangle is equal to the exterior angle of third vertex.

By using exterior angle property of a triangle,

Subtract both sides by 15.

The measure of ∠NOP  is 15 degree. Therefore option B is correct.

place r′ so that qr′ is parallel to the tangent.

now we get that ∠r′py=∠pr′q, where y is on the tangent, on the opposite side of p from x.

also, because of the symmetry, ∠r′py=∠qpx.

finally, note that no matter where we place r, as long as it's on the correct arc, we have ∠prq=∠pr′q.

stringing all these equalities together, we end up with ∠prq=∠qpx.

this picture will show how its going to look like.

hope this by jack monhen