Question

Two parallel lines are crossed by a transversal.

Answer 1

When a pair of parallel lines is intersected by a transversal, then

Corresponding angles are equal.

∠2 and ∠6 are corresponding angles.

So, m∠2 = m∠6

=> m∠2 = 123.5°

We know that linear pair of angles are supplementary (180°).

∠1 and ∠2 are linear pair of angles.

So, m∠1 + m∠2 = 180°

=> m∠1 + 123.5° = 180°

=> m∠1 = 180° - 123.5°

=> m∠1 = 56.5°

Answer 2

Answer:

${ \boxed{ \tt{m \angle1 = m \angle5}}} \\ { \tt{m \angle1 = 180 \degree - m \angle6}} \\ { \tt{m \angle1 = 180 \degree - 123.5 \degree}} \\ { \bf{m \angle1 = 56.5 \degree}}$