Question

In the given figure, $L_1||L_2$ and $L3$ is the transversal. Which of the following is true?

• A. ∠4 + ∠6 = 180°
• B. ∠2 + ∠7 = 180°
• C. ∠4 + ∠3 – ∠1 = ∠2
• D. ∠8 + ∠1 = 180°

Answer 1

The correct option is C ∠4 + ∠3 – ∠1 = ∠2


Since $L_1||L_2$ and $L_3$ is the transversal.
∴ ∠4 = ∠6 (Alternate interior angles)
Also, ∠2 = ∠6 (Corresponding angles)
And, ∠6 = ∠7 (Vertically opposite angles)
∴ ∠2 = ∠7
Similarly, ∠1 = ∠5 (Corresponding angles)
and ∠5 = ∠8 (Vertically opposite angles)
∴ ∠1 = ∠8
Since $L_3$ is not necessarily always perpendicular to $L_1$ and $L_2$.
$\therefore \angle 4+\angle 6\ne {180}^{\circ }$
and, $\angle 2+\angle 7\ne {180}^{\circ }$
and, $\angle 1+\angle 8\ne {180}^{\circ }$
Now, ∠4 = ∠2 and ∠3 = ∠1 (Vertically opposite angles)
∴ ∠4 + ∠3 = ∠2 + ∠1 (Adding ∠4 = ∠2 and ∠3 = ∠1)
⇒ ∠4 + ∠3 – ∠1 = ∠2
Hence, the correct answer is option (c).