Question

Find the value of each variable in the circle to the right. The dot represents the center of the circle.

Answer 1

9514 1404 393

Answer:

  a = 57.5

  b = 90

  c = 65

Step-by-step explanation:

The measure of an inscribed angle is half that of the arc it intercepts. The angle at 'a' intercepts an arc of 115°, so its measure is (115/2)° = 57.5°

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The inscribed angle at 'b' is a semicircle, 180°, so the measure of 'b' is (180/2)° = 90°.

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The arc 'c' is the remainder of a semicircle after 115° have been taken away. Its measure is 180° -115° = 65°.

  (a, b, c) = (57.5, 90, 65)