Mathematics

Problem

Three lines

l_1,\, l_2

and

l_3

pass through the same point

O

. It is given that

l_1 \perp l_2

and the acute angle between

l_2

and

l_3

35^{\circ}

. a. (i) Draw a neat labelled sketch showing the three lines and the given information. b. (ii) Using angle relationships at a point, prove that the acute angle between

l_1

and

l_3

55^{\circ}

. c. (iii) If

l_3

is now rotated about

O

so that it makes an angle of

y^{\circ}

with

l_1

towards the opposite side of the angle calculated in part (ii), find—giving full justification—the measure of the angle between

l_2

and the new position of

l_3

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