Lines and are parallel and are intersected by a transversal at points and

MATHEMATICS · Multi-part · CBSE · Mathematics · Lines and Angles · Lines and Angles

Problem

Lines

l

and

m

are parallel and are intersected by a transversal

p

at points

P

and

Q

. At

P

, one of the angles formed is

(5x+15)^{\circ}

. The angle vertically opposite to this angle at

P

(7x-45)^{\circ}

. (i) Find the value of

x

. (ii) Using this value of

x

, determine the measure of all four angles formed at point

P

. (iii) Hence, state the measure of the angle at

Q

that corresponds to the angle

(5x+15)^{\circ}

P

, giving a brief reason for your answer.