Parallel lines angles

I need help with the following sat math geometry question:

"In the figure below, a Transversal crosses two parallel lines l and p. Find the value of x"

39

Thanks

kadence

07-27-2013, 12:58 PM

Parallel lines angles question

I need help with the following sat math geometry question:

"In the figure below, a Transversal crosses two parallel lines l and p. Find the value of x"

39

Thanks

Definitions

A transversal is a line that interesects two or more lines.

Alternate interior angles are two non adjacent interior angles on opposite sides of a transversal.

Alternate exterior angles are two non adjacent exterior angles on opposite sides of a transversal.

Corresponding angles are two non adjacent exterior angles on the same side of a transversal such that one is an exterior angle and the other is an interior angle.

Same side interior angles are two non adjacent interior angles on the same side of a transversal.

Linear pairs are two adjacent angles which are supplementary ( are pairs of angles that add up to 180 degrees).

Vertical angles are two non adjacent angles formed by a pair of intersecting lines that share a vertex.

Also holds the following propositions:

If two parallel lines are cut by a transversal, the alternate interior angles are congruent.

If two lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel.

If two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel.

If two parallel lines are cut by a transversal, the corresponding angles are congruent.

If two lines are cut by a transversal and the corresponding angles are congruent, the lines are parallel.

If two parallel lines are cut by a transversal, the interior angles on the same side of the transversal are supplementary.

If two lines are cut by a transversal and the interior angles on the same side of the transversal are supplementary, the lines are parallel.

If two angles form a linear pair, they are supplementary.

Vertical angles are congruent.

So, regarding to your question the two angles are supplementary

(3x)+(x-40)=180\Rightarrow 4x=180+40 \Rightarrow 4x=220 \Rightarrow x=55^o

Hope these help!!;);)

Thank you for your detailed answer!!

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