A circle is shown. A secant and a tangent intersect at a common point outside of the circle to form an angle that measure 51 degrees. The measure of the first arc formed is x degrees and the measure of the second arc formed is 160 degrees.
What is the value of x?

x =

when a secant and a tangent meets outsides of a circle, the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs. Therefore,

51° = 1 / 2 (160 - x)

Therefore,

51 = 80 - x / 2

51 - 80 = - 1 /2 x

-29 = - 1 / 2 x

multiply both sides by -2

-29 × 2 = - 1 / 2 x × -2

x = 58

Therefore, the value of x is 58 degrees

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A circle is shown. A secant and a tangent intersect at a common point outside of the circle to form an angle that measure 51 degrees. The measure of the first arc formed is x degrees and the measure of the second arc formed is 160 degrees. What is the value of x? x =

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Secant and tangent intersection

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A circle is shown. A secant and a tangent intersect at a common point outside of the circle to form an angle that measure 51 degrees. The measure of the first arc formed is x degrees and the measure of the second arc formed is 160 degrees.
What is the value of x?

x =