Mathematics

Problem

Lines MN and PQ intersect at point O. One pair of opposite angles has measures

\angle MON = (4y + 27)^{\circ}

and

\angle QOP = (2y + 57)^{\circ}

. a. (i) Set up an equation in

y

using the relationship between these two angles. b. (ii) Determine the value of

y

and calculate the measure of all four angles formed at O. c. (iii) Verify that each pair of opposite angles is equal and each pair of adjacent angles is supplementary.

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