Question

Which equation is correct regarding the measure of ∠mnp? m∠mnp = one-half(x – y) m∠mnp = one-half(x y) m∠mnp = one-half(z y) m∠mnp = one-half(z – y)

Answer 1

The measure of anle MNP is

• m ∠ MNP = (x - y)/2

Step-by-step explanation:

The image attached shows the figure corresponding to this question.

The angle MNP, wich is also the angle LNP, is formed by the intersection of a secant and a tanget to a circle.

Then, you can use the theorem:

• the angle formed by a secant and a tangent to a circle that intersect outside the circle is half the difference of the major arc minus the minor arc.

The major arc formed is identified with the letter x and the minor arc is identified witht he letter y. Thus, the measure of the angle MNP is half the differenc x - y:

• m ∠ MNP = (x - y)/2