Mathematics

Problem

Two straight lines GF and HK intersect at point O forming four angles labelled consecutively in clockwise order as

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

and

\angle 4

. It is given that

\angle 1 : \angle 2 = 3 : 2

and

\angle 2 : \angle 3 = 2 : 3

. a. (i) Express

\angle 1, \angle 2,

and

\angle 3

in terms of a single variable

k

. b. (ii) Using the fact that

\angle 1

and

\angle 2

form a linear pair, find the value of

k

. c. (iii) Determine the measures of

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

and

\angle 4

and verify that the two pairs of opposite angles are equal.