Mathematics

Problem

Lines

GH

and

JK

intersect at point

P

. The measure of

\angle GPJ

(2y + 10)^\circ

. The angle adjacent to it,

\angle HPJ

, measures

(3y - 20)^\circ

. a. (i) Form an equation in

y

using appropriate angle relationships and the given expressions. b. (ii) Solve the equation formed in part (i) to find the value of

y

. c. (iii) Hence, calculate the measure of all four angles formed at point

P

and state whether each is acute or obtuse, providing justification.