Question

In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.​

Answer 1

angle 1 = 60°

angle 6 = 120°

angle 5 = 180° - 120° = 60°

Since angle 1 and angle 5 are equal (corresponding angles).

So lines m and n are parallel.

Answer 2

★ Figure refer to attachment

Given

• ∠1 = 60°
• ∠6 = 120°

To prove

• m l l n

Proof

➡ ∠ 1 + ∠ 2 = 180 {Linear pair}

➡ 60 + ∠ 2 = 180

➡ ∠ 2 = 180 - 60

➡ ∠ 2 = 120°

∠2 = ∠6 {Alternate interior angle}

∴ m l l n

Additional Information

*If a transversal cuts a pair of the lines in such a away that

(★) the angle of any pair of corresponding angles are equal or

(★) the angles of any pair of alternate interior (or exterior) angles are equal or

(★) the angles of any pair of interior angles on the same side of transversal are supplementary,

then the lines are PARALLEL.

$\rule{200}3$