Question

In the diagram below, xy and yz are tangent to O. What is the measure of angle y

Answer 1

Answer: c. 48°

Explanation:

From the diagram above, taking the circle in an anti-clockwise direction, we can say, ZX =228° and XZ = 132°

Using the outside angle theorem;

<y = (ZX - XZ) / 2

<y = (228 - 132) / 2

<y = 96 / 2

<y =48°

Therefore, the measure of angle y is 48°

Answer 2

If we draw in OX, OY, OZ we have two congruent right triangles, right angles at the tangent points.

We know XOZ is 132 degrees, which is the meaning of the arc measure

So YOX is half that, 66 degrees.

That leaves 180 - 90 - 66 = 24 degrees for OYX

Angle Y aka XYZ is double that, 48 degrees.

Answer: C