SOLUTION: Lines AB and CD are parallel to each other. Inside the lines AB and CD, there is a point P and an angle P consisted of segment XP and segment PY (XP and PY form an acute angle). Th

Algebra ->  Points-lines-and-rays -> SOLUTION: Lines AB and CD are parallel to each other. Inside the lines AB and CD, there is a point P and an angle P consisted of segment XP and segment PY (XP and PY form an acute angle). Th      Log On


   

Question 1096896: Lines AB and CD are parallel to each other. Inside the lines AB and CD, there is a point P and an angle P consisted of segment XP and segment PY (XP and PY form an acute angle). The acute angle that XP and AB form is 35 degrees. The acute angle that PY and CD form is 42 degrees. What is the measure of angle P?
Sorry if this question is a bit unclear! If it's possible, can you also tell me how to make graphs in questions? Thank you!
Found 2 solutions by KMST, greenestamps:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!


Let us extend segment PX until it meets line CD at point green%28Z%29 :



Angle PYC is the same angle as PYZ (just called by a different name),
and measures 42%5Eo .
Angle AXP is the same angle as AXZ (just called by a different name),
and measures 35%5Eo .
Angle XZD is congruent to angle as AXZ ,
because they are alternate interior angles.
So, angle XZD=PZY measures 35%5Eo too.
The angle at P, angle XPY is an exterior angle to traingle PYZ ,
and as all exterior angles to a triangle,
its measure is the sum of the measures of the non-adjacent interior angles of the triangle
(in this case angles PZY and PYZ ).

So, the measure of angle XPY is 35%5Eo%2B42%5Eo=highlight%2877%5Eo%29 .

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!

I have seen many students who like to solve this problem by the method shown by the other tutor. I find it easier to see the solution by a different method, which I have also seen many students use. Use the one which makes the most sense to you.

Here is the diagram of the problem from the other tutor:




And here is what I do with the diagram to solve the problem.

Draw line EF through P parallel to AB and CD.


Now angle XPF is congruent to angle PXA, and angle YPF is congruent to angle PYC. So the measure of angle P is just 35 degrees plus 42 degrees = 77 degrees.