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

Question 517793: Two lines intersect to form two pairs of vertical angles. Angle 1 with measure (20x + 7) degrees and angle 3 with measure (5x + 7y + 49) degrees are vertical angles. Angle 2 with measure (3x - 2y + 30) degrees and angle 4 are vertical angles. Find the values x and y and the measure of all four angles.
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Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two lines intersect to form two pairs of vertical angles.
Angle 1 with measure (20x + 7) degrees and angle 3 with measure (5x + 7y + 49) degrees are vertical angles.
Angle 2 with measure (3x - 2y + 30) degrees and angle 4 are vertical angles. Find the values x and y and the measure of all four angles.
:
We know that adjacent angles = 180, so using Angles 1 & 2, write an equation:
(20x+7) + (3x-2y+30) = 180
20x + 3x - 2y + 7 + 30 - 180
23x - 2y = 180 - 37
23x - 2y = 143
:
Angle 4 = Angle 2, using adjacent angles 3 & 4, write another equation
(5x+7y+49) + (3x-2y+30) = 180
5x + 3x + 7y - 2y + 49 + 30 = 180
8x + 5y = 180 - 79
8x + 5y = 101
:
Multiply the 1st equation by 5, multiply the 2nd equation by 2
115x - 10y = 715
16x + 10y = 202
------------------addition eliminates y, find x
131x = 917
x =
x = 7
:
Find y using: 8x + 5y = 101
8(7) + 5y = 101
56 + 5y = 101
5y = 101 - 56
5y = 45
y =
y = 9
:
Angle 1, 20x+7; 20(7) + 7 = 147 degrees
Angle 2, 3x-2y+30; 3(7) - 2(9) + 30 = 33 degrees
:
Note that Angles 1 & 2 add up to 180 degrees, Angles 3 and 4 should be the same
Angle 3, 5x+7y+49; 5(7) + 7(9) + 49 = 147 degree
Angle 4, 3x-2y+30; 3(7) - 2(9) + 30 = 33 degrees
:
Summarize: x=7, y=4, Angles 1*3 = 147, Angles 2&4 = 33
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