Mathematics

Problem

Lines

EF

and

GH

intersect at

O

. In clockwise order, the first three angles are given by

\angle 1 = (2x+y)^\circ

\angle 2 = (3y-20)^\circ

\angle 3 = (4x - y + 10)^\circ

. a. (i) Form two linear equations in

x

and

y

by using suitable relationships among the angles at

O

. b. (ii) Solve the equations to obtain the values of

x

and

y

. c. (iii) Find the measure of

\angle 4

. d. (iv) Classify

\angle 3

as acute, right, obtuse, or straight, giving a reason.