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Question 494256: Parallel postulates and special angles problem:
Given: l is parallel to m and transversal t,
m<1 = 4x + 2
m<6 = 4x - 2
Find: x and M<5
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! We would need to know the locations of the angels, such as alternate interior, corresponding, etc.
Cleomenius.
Ok, now that I see the diagram , angles 1 and angle 6 are called exterior angles on the same side of the transversal, they are supplemental and together equal 180 degrees.
So, 4x +2 +4x -2 = 180
8x = 180 degrees.
x = 22.5
Angle 1 is 4(22.5) + 2 = 92
Angle 5 is 4(22.5) - 2 = 88
92 degrees + 88 degrees = 180 degrees.
Angle 5 is a supplemental angle to angle 6, it is an adjacent angle on a straight line of 180 degrees. Therefore it is 92 degrees.
It is also a corresponding angle to angle 1, it is a corollary if two parallel lines are cut by a transversal, then each pair of corresponding angles formed is congruent.
Cleomenius.
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