Question

What is the measure of XZ shown in the diagram below?

Answer 1

Answer:

C

Step-by-step explanation:

The secant- secant angle VYW is calculated as

∠VYW = 0.5( arc VW - arc XZ ), that is

35° = 0.5 (84 - XZ )

35  = 42 - 0.5XZ ( subtract 42 from both sides )

- 7 = - 0.5XZ ( divide both sides by - 0.5 )

14 = XZ

That is arc XZ = 14° → C

Answer 2

Answer:

14°

Step-by-step explanation:

Here we need to use the theorem, which states:

"An angle formed by two secants is one-half the difference of its intercepted arcs"

In this case, the angle created is 35°, and the intercepted arcs are XZ and VW = 84°.

According to this theorem, we have

$35\°=\frac{1}{2}(arc(VW) - arc(XZ))\\ 35=\frac{1}{2}(84-arc(XZ))\\ 35=42-\frac{XY}{2}\\ \frac{XY}{2}=42-35\\XY=2(7)14\°$

Therefore, according to the theorem, the arc XZ is 14°.