Question

Please use the following image below in order to answer the question:

Find the value of x.

What is the value of X?

Please show all of the work on how you got your answer. (Note: If you can't explain your work then that's completely fine. All I am asking for is the work shown with your answer)

Answer 1

11

Explanation:

6x - 11 + 125 = 180

6x = 66

x = 11°

Answer 2

x = 11

Explanation:

Consider the attached drawing. The central angle at C has the same measure as the arc: 125°. XYCZ is a quadrilateral, so has a sum of interior angles that is 360°. The interior angles are tangent points Y and Z are both 90°, so the remaining two angles are supplementary.

That is ...

(6x -11)° +125° = 180°

6x = 66 . . . . . . subtract 114

x = 11 . . . . . . . . .divide by 6

__

So, the things you need to know about this geometry are ...

• tangents are 90° to the radius at the tangent point
• the sum of angles in a quadrilateral is 360°
• the measure of an arc is the same as that of its central angle

In short: the angle at X and the arc YZ are supplementary: they have a sum of 180°.