Answer:
140°
Step-by-step explanation:
Short answer: x is the supplement of 40°, so is 140°.
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Longer answer: The sum of angles of a quadrilateral is 360°. The angle where the radius meets the tangent line is 90°, so you have ...
x + 90 + 40 + 90 = 360
x = 140 . . . . subtract 220 from both sides
You will note that if you subtract 180 first you have ...
x + 40 = 180 . . . . . . x° and 40° are supplementary
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A little bit longer answer: The measure of the angle where the tangents meet is half the difference of the intercepted arcs. That is ...
40° = (1/2)·((360°-x°) - x°)
40° = 180° -x° . . . . . . . . . . by now, this should look familiar
x° = 180° -40° = 140°
