Mathematics

Problem

Lines

AB

and

CD

intersect at point

O

. Ray

OE

lies inside

\angle AOC

and bisects it. The measure of

\angle BOE

(4z - 8)^\circ

and the measure of

\angle BOD

(7z + 2)^\circ

. a. (i) Express

\angle AOE

and

\angle COE

in terms of

z

. b. (ii) Using suitable angle relationships, form an equation in

z

and solve it. c. (iii) Determine the measure of

\angle COE

and state whether this angle is acute, right, obtuse, or straight, giving appropriate reason.