Question 407376: ABCD is a parallelogram. < A=(7y+x), < B= (2x-5), and < D=(3y-12) Find measures of < A,< B,< C,< D.
Thank you!
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Fact #1: The sum of all 4 angles in ANY parallelogram (or any quadrilateral for that matter) is ALWAYS 360 degrees.
Fact #2: The opposite angles in any parallelogram are ALWAYS congruent (ie equal)
Fact #3: The adjacent angles in any parallelogram are ALWAYS supplementary (ie they add to 180 degrees)
Use the fact stated above to form the equation
< A + < B + < C + < D = 360
(7y+x) + (2x-5) + < C + (3y-12) = 360
3x+10y-17 + < C = 360
So we have one equation 3x+10y-17 + < C = 360. Call it equation 1.
Now use fact #2 to note that < B = < D (draw a picture if you can't see this). So 2x-5 = 3y-12, which is another equation. Call it equation 2.
Finally, use fact #3 to get the equation
< A + < B = 180
(7y+x)+(2x-5)=180
3x+7y-5=180
So equation 3 is 3x+7y-5=180
So your goal is to now solve equations (2) and (3) simultaneously (these two equations form a system of equations). Doing this will give you the values of x and y. Once you have x and y, you can plug them into equation (1) to find angle < C. Also, the values of x and y will help you find the other angles.
If you need more help, email me at jim_thompson5910@hotmail.com
Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you
Jim
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