Lines AB and CD intersect at point O

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

Problem

Lines AB and CD intersect at point O. The measures of two opposite angles at O are given by

\angle AOC = (3x + 10)^{\circ}

and

\angle BOD = (5x - 50)^{\circ}

. (i) Form an algebraic equation in

x

using the relationship between the given angles. (ii) Solve for

x

and hence find the measure of each of the four angles formed at O. (iii) State whether

\angle AOC

is acute, right, obtuse or reflex, giving reason for your answer.