SOLUTION: Two lines intersect to form two pairs of vertical angles. angle 1 with measure (20x+7)� and angle 3 with measure (5x + 7y + 49)� are vertical angles. angle 2 with measure (3x

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Question 1033457: Two lines intersect to form two pairs of vertical angles. angle 1 with measure (20x+7)� and angle 3 with measure (5x + 7y + 49)� are vertical angles. angle 2 with measure (3x - 2y + 30)� and angle 4 are vertical angles. Find the values x and y and the measures of all four angles.
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
the vertical angles are equal.

you get 20x + 7 = 5x + 7y + 49
subtract (5x + 7y + 49) from both sides of the equation to get:
15x - 7y - 42 = 0
add 42 to both sides of this equation to get:
15x - 7y = 42

the adjacent angles are supplementary.

you get 20x + 7 + 3x - 2y + 30 = 180
combine like terms to get:
23x - 2y + 37 = 180
subtract 37 from both sides of this equation to get:
23x - 2y = 143

you have 2 equations that need to be solved simultaneously.
they are:
15x - 7y = 42
23x - 2y = 143

once you solve these 2 equations simultaneously, you will find that:
x = 7 degrees.
y = 9 degrees.

once you replace x and y in the original equations with 7 and 9, you will find that the original equations are true.

this will confirm that your solution is correct.

if you have any question on how to do any of what i described above, let me know and i will instruct you further.