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How do I figure this out?

How do I figure this out?-example-1

1 Answer

3 votes

Answer:

140°

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°

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