Corresponding Angles: in Parallel Lines

A transversal is a line
that passes through two lines.

By two lines and a transversal,
four pairs of corresponding angles are formed.

∠1 and ∠1'
∠2 and ∠2'
∠3 and ∠3'
∠4 and ∠4'

Corresponding angles in parallel lines
are congruent.

m∠1 = m∠1'
m∠2 = m∠2'
m∠3 = m∠3'
m∠4 = m∠4'

The given angles are
corresponding angles in parallel lines.

So the given angles are congruent.

So [7x + 1] = [64].

Move +1 to the right side.

Divide both sides by 7.

Then x = 9.

So x = 9.

These two horizontal lines are parallel.

So the right angles are
corresponding angles in parallel lines.

So these two angles are congruent.

Next, these two inclined lines are parallel.

So the bottom angles are also
corresponding angles in parallel lines.

So these two angles are congruent.

These three angles are all congruent.

So [14x - 3] = [8x + 45].

Move -3 to the right side
and move 8x to the left side.

Then,
14x - 8x, 6x
is equal to,
45 + 3, 48.

Divide both sides by 6.

Then x = 8.

So x = 8.