Question

Please help!!

A, B, C and D are points on the circumference of a circle, centre O. Angle BAD = 112° and angle DCO = 33° D A N 112° B y 33° с Calculate the value of z. Not to scale

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Answer 1

z = 55°

Explanation:

Opposite angles of an inscribed quadrilateral are supplementary.

m<A + m<DCB = 180°

m<DCB = 180° - 112°

m<DCB = 68°

m<DCO + m<OCB = 68°

m<OCB = 68° - 33°

m<OCB = 35°

y = m<OCB = 35° (since in triangle OBC, OB = OC)

m<BOC + y + m<OCB = 180°

m<BOC = 180° - 35° - 35°

m<BOC = 110°

m(arc)BC = m<BOC = 110°

z = (1/2)m(arc)BC = (1/2)(110°) = 55°