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=(1)/(2)(\widehat{\text fararc }-\widehat{\text near arc})`

Now substituting given values in our formula we will get

`m\angle x=(136^(0)-28^(0))/(2)=(108^(0))/(2)=54^(0)`

Therefore, measure of angle x is 54 degrees.