Question

In the adjoining figure, line a || line b. line l is a transversal. Find the measures of ∠x, ∠y, ∠z using the given information.

Answer 1

Let us mark the points A and B on l; K and M on a; L and N on b.
Suppose KM and LN intersect AB at P and Q respectively.
Since, a || b and l is a transversal, then
m∠ PQL = m∠ APK    (Corresponding angles)
⇒ x = 105°
Since AB and LN are straight lines that intersect at Q, then
m∠ BQN = m∠ PQL    (Vertically opposite angles)
⇒ y = x
⇒ y = 105°
Since AB is a straight line and ray QN stands on it, then
m∠ BQN + m∠ PQN = 180°    (Angles in linear pair)
⇒ y + m∠ PQN = 180°
⇒ 105° + m∠ PQN = 180°
⇒ m∠ PQN = 180° − 105°
⇒ m∠ PQN = 75°
Now, m∠ APM = m∠ PQN    (Corresponding angles)
⇒ z = 75°