Question

1. Choose the correct alternative.
(1) In the adjoining figure, if line m ∥ line n and line p is a transversal then find x.

(A) 135$°$
(B) 90$°$
(C) 45$°$
(D) 40$°$

(2) In the adjoining figure, if line a ∥ line b and line l is a transversal then find x.

(A) 90$°$
(B) 60$°$
(C) 45$°$
(D) 30$°$

Answer 1

(1)

Let us mark the points P and Q on m; R and S on n; A and B on p.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since, m||n and p is a transversal, then
m∠QMN + m∠SNM = 180° (Interior angles on the same side of transversal are supplementary)
Substituing the values in the above equation, we get
3x + x = 180°
⇒ 4x = 180°
⇒ x = $\frac{180°}{4}$
∴ x = 45°
So, the correct answer is option (C).

(2)

Let us mark the points P and Q on a; R and S on b; A and B on l.
Suppose PQ and AB intersect at M; RS and AB intersect at N.
Since a||b and l is a transversal, then
m∠RNM = m∠SNB (Vertically opposite angles)
⇒ ∠RNM = 2x
Now, m∠RNM + m∠PMN = 180° (Interior angles on the same side of transversal are supplementary)
⇒ 2x + 4x = 180°
⇒ 6x = 180°
⇒ x = $\frac{180°}{6}$
⇒ x = 30°
So, the correct answer is option (D).