Question

Find the value of Z in the picture

Answer 1

Answer: OPTION B.

Explanation:

It is important to remember that:

`Tangent\ chord\ angle=(1)/(2)(Intercepted\ arc)`

We can identify in the figure that 94° is the measure of a tangent chord angle. Then, we can find "x":

`94\°=(1)/(2)x\\\\(2)(94\°)=x\\\\x=188\°`

Since there are 360° in a circle, we can subtract 360° and the value of "x" to find the value of "z". Then we get:

`z=360\°-x\\\\z=360\°-188\°\\\\z=172\°`

Answer 2

172°

Explanation:

Connect the center of the circle with two endpoints of the chord. You'll get the isosceles triangle with the angles adjacent to the base of

`94^(\circ)-90^(\circ)=4^(\circ)`

Then the angle between two congruent sided (two radii of the circle) is

`180^(\circ)-2\cdot 4^(\circ)=172^(\circ)`

This angle is central angle subtended on the arc z, so the measure of z is 172°.