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Max
07-27-2013, 01:39 PM
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, 01:58 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!!;);)

Max
07-27-2013, 02:04 PM
Thank you for your detailed answer!!