Question

In the figure below, X Z is a diameter of circle A.

What is the arc measure of minor arc Y Z in degrees?

Answer 1

mYZ = 59°

Explanation:

If XZ is a diameter is forms a semicircle with it's arc degree half of that of the circle, in other words 180°. That would mean:

m∠ ZAY + m∠ YAX = 180,

( 5w + 4 ) + ( 11w ) = 180,

11w + 5w + 4 = 180,

16w = 176,

w = 11°

Now mYZ is, in other words, m∠ ZAY, so let us solve for m∠ ZAY:

m∠ ZAY = 5w + 4,

m∠ ZAY = 5 * ( 11 ) + 4,

m∠ ZAY = 55 + 4,

m∠ ZAY = 59°,

mYZ = 59°