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Help with parallel lines plz

0
30
5
+1747

Help how do you do this

Jan 12, 2024

#1
+290
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By Triangle Angle Sum Theorem, the interior angle E is 180 - 40 - 80 = 60 degrees.

The angle adjacent to angle E is 180 - 60 = 120 degrees

By the Same-Side Interior Angles Postulate, 120 + x = 180 since they are supplementary to each other

x = 60 degrees

Jan 12, 2024

#1
+290
+1

By Triangle Angle Sum Theorem, the interior angle E is 180 - 40 - 80 = 60 degrees.

The angle adjacent to angle E is 180 - 60 = 120 degrees

By the Same-Side Interior Angles Postulate, 120 + x = 180 since they are supplementary to each other

x = 60 degrees

DS2011 Jan 12, 2024
#2
+25
0

x = 40.

I created a third line that is parrellel to the first two. Then, I extended line GH.

Since vertical lines are congruent, the 80 degress reflects down. Then, using corresponding angles congruent, we have the angle next to the bottom 80 as 40.

Then, using corresponding angles again, we have x = 40.

Sorry, this might be confusing because I don't know how to make a picture.

Jan 12, 2024
#4
+290
+1

I think I know what you are saying, and that is Extending GH and then the vertical angle is 80 degrees, but I am not sure where 40 degrees came from. If you tried 180 - 80, you would get 100. Also, note that GH and CD would not be parallel to each other.

DS2011  Jan 12, 2024
edited by DS2011  Jan 12, 2024
#3
+290
+1

Actually, when finding that angle E is 60 degrees, you could use the Alternate Interior Angles Theorem that states that the two angles that are alternate interior angles are congruent to find that 60° ≅ x, so x = 60 degrees

Skipped 1 step this way.

Jan 12, 2024