Three lines ,

MATHEMATICS · Multi-part · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Three lines

a

b

, and

c

are parallel and are cut by a transversal

p

. At the point where

p

meets

a

, the angle on the right of

p

and above

a

35^{\circ}

. A second transversal

q

intersects

a

b

, and

c

at points

M

N

, and

O

respectively, making a right angle at

N

. (i) Find the angle on the left of

p

and below

b

. Give reason for your answer. (ii) Determine the angle that

q

makes with

a

. State the theorem used. (iii) Calculate the acute angle between transversals

p

and

q

. Record the sequence of angle relationships you have employed.