Mathematics

Problem

Lines

MN

and

PQ

intersect at

O

. One of the four angles is

(4x-20)^\circ

. The angle adjacent to it is

(3x+5)^\circ

. Denote these two angles as

\angle a

and

\angle b

respectively. a. (i) Find the value of

x

. b. (ii) Determine the measure of each of the four angles formed at

O

. c. (iii) State whether each of the four angles is acute, right, obtuse, or straight.