Mathematics

Problem

Two lines

\ell

and

m

are perpendicular and intersect at point

O

. A third line

n

also passes through

O

making an acute angle with

\ell

. a. (i) If the acute angle

\angle \ell ON=(5y-11)^\circ

and its adjacent angle

\angle mON=(3y+41)^\circ

, find the value of

y

. b. (ii) Hence calculate the measures of

\angle \ell ON

and

\angle mON

. c. (iii) Find the measures of all the remaining angles formed at

O

by the three lines

\ell

m

, and

n