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Line m is tangent to the circle. Find the indicated measure

Line M Is Tangent To The Circle Find The Indicated Measure class=

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Answer:

  105°

Step-by-step explanation:

The measure of an inscribed angle is half the measure of the arc it subtends. For an arc of 210°, an inscribed angle that subtends it will have a measure of 105°.

We normally think of the sides of an inscribed angle as being a chord. However, that chord can be considered part of a secant. When the two points of intersection with the circle get arbitrarily close together, the chord becomes a point, and the secant becomes a tangent.

That is, the angle made by this geometry is simply a degenerate case of an inscribed angle. The relationship with the arc measure is unchanged.

  m∠1 = 105°

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