Question

Find the value of Z in the picture

Answer 1

Answer:

172°

Step-by-step 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°.

Answer 2

Answer: OPTION B.

Step-by-step explanation:

It is important to remember that:

$Tangent\ chord\ angle=\frac{1}{2}(Intercepted\ arc)$

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

$94\°=\frac{1}{2}x\\\\(2)(94\°)=x\\\\x=188\°$

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:

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