Question

What is the value of x? 54 68 56 82

Answer 1

136-28 = 108
108/2 = 54
Answer : 54

Answer 2

We have been given two secants and their intercepted arc measures and we are asked to find the measure of angle x.

In order to find measure of angle x we will use circle's two intersecting secants from a point theorem. This theorem tells us that measure of an angle  formed by two secants drawn from an outside point equals to half the difference of intercepted arcs.

$m\angle x=\frac{1}{2}(\widehat{\text fararc }-\widehat{\text near arc})$

Now substituting given values in our formula we will get

$m\angle x=\frac{136^{0}-28^{0}}{2}=\frac{108^{0}}{2}=54^{0}$

Therefore, measure of angle x is 54 degrees.