Lines and intersect at point

MATHEMATICS · Single correct · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Lines

JK

and

LM

intersect at point

O

, forming four angles that are numbered clockwise as

\angle 1, \angle 2, \angle 3,

and

\angle 4

. The following relations are given:

\angle 1 = (x + 20)^\circ

\angle 2 = (2y - 5)^\circ

\angle 3 = (3x - 10)^\circ

Find the measure of

\angle 4

. (a)

155^{\circ}

(b)

145^{\circ}

(c)

35^{\circ}

(d)

120^{\circ}