Question

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

Answer 1

14°

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\°=(1)/(2)(arc(VW) - arc(XZ))\\ 35=(1)/(2)(84-arc(XZ))\\ 35=42-(XY)/(2)\\ (XY)/(2)=42-35\\XY=2(7)14\°`

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

Answer 2

C

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