Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 weeks ago

Find angle the missing angle?

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  • 2 weeks ago
    Favorite 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.

  • JOHN
    Lv 7
    2 weeks ago

    M = 95

    βθω = 50

    θωP = 90 (angle in a semicircle)

    θPω = 85

    Pθω = 5

    Pωμ = 55

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