SOLUTION: x, y, and z are points on a line angles are formed by line segments yu, yw angle wyx=2(12b+7) and angle zyu=9b-1, find angle uyw. good luck. i know i need it.

Question 212351: x, y, and z are points on a line
angles are formed by line segments yu, yw
angle wyx=2(12b+7) and angle zyu=9b-1, find angle uyw.
good luck. i know i need it.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
angle wyx=2(12b+7) = 24b + 14
angle zyu = 9b-1
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xyz are points on a line. x is on the left, y is in the middle, z is on the right.
draw 2 points above the line.
left point is w and right point is u.
make a line from w to y and from u to y.
looks like they form a v with w being the left top of the v and u being the right top of the v and y being the bottom of the v.
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these lines form 3 angles that when added together are equal to 180 degrees.
these angles are:
wyx is the left angle
wyu is the middle angle
uyz is the right angle
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wyx = 2 * (12b+7) = 24b + 14 (given)
uyz = 9b-1 (given)
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this makes angle wyu = 180 - (24b+14) - (9b-1)
this becomes:
wyu = 180 - 24b - 14 - 9b + 1 which becomes:
wyu = 180 - 33b - 13 which becomes:
wyu = 167 - 33b
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the 3 angles when added together should equal 180.
24b + 14 + 9b - 1 - 33b + 167 equals:
33b - 33b + 167 + 13 which equals:
180
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this confirms the calculations are good and that angle wyu = 167 - 33b
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