Lines MN and PQ intersect at point O

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

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}

. (i) Set up an equation in

y

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

y

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

Related theory

Lines and Angles
Triangle congruence
Pairs of angles

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