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# Find angle the missing angle?

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- stanschimLv 72 weeks agoFavorite Answer
Arc βθ is 70 degrees since the inscribed angle that intercepts it is 35 degrees (an inscribed angle is 1/2 its intercepted arc).

20 degrees = 1/2(arc βθ - arc ωρ) since an external angle intercepting a circle must be 1/2 the difference of the intercepted arcs.

20 degrees = 1/2(70 - arc ωρ)

40 = 70 - arc ωρ

arc ωρ = 30 degrees.

Now, since there are 180 degrees in a semi-circle, arc βω must be 180 - 70 - 30 = 80 degrees.

Angle βθω is 1/2 of 80 = 40 degrees since it is an inscribed angle intercepting arc βω.

Angle M = 180 - 35 - 40 = 180 - 75 = 105 degrees since the angles of a triangle total to 180 degrees.

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