GEOMETRY

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ABCD is an inscribed quadrilateral. AD, BC are produced to meet at X. If angle B= 80 degrees and angle X= 30 degrees, find angle XCD.

  • GEOMETRY -

    I will assume you mean "inscribed in a circle"
    In a cyclic quadrilateral, the opposite angles are supplementary, so angle D = 100°
    Also angle ADC is an exterior angle in triangle DCX, so
    angle DCX + angle CXD = angle ADC
    angle DCX + 30 = 100
    angle DCX = 70°

  • GEOMETRY -

    30

  • GEOMETRY -

    50 degrees

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