Answer:
x = 11
Step-by-step 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
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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°.
