SOLUTION: In a quadrilateral JKLM, measure angle J=x,measure angle K=2x, measure angle L=2x+10,and measure angle M=3x-5. Find the measure of the angle.

Algebra ->  Triangles -> SOLUTION: In a quadrilateral JKLM, measure angle J=x,measure angle K=2x, measure angle L=2x+10,and measure angle M=3x-5. Find the measure of the angle.      Log On


   

Question 119555: In a quadrilateral JKLM, measure angle J=x,measure angle K=2x, measure angle L=2x+10,and measure angle M=3x-5. Find the measure of the angle.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
For any quadrilateral, the sum of the 4 angles is 360 degrees. So in this case, J%2BK%2BL%2BM=360


J%2BK%2BL%2BM=360 Start with the given equation


x%2B2x%2B2x%2B10%2B3x-5=360 Plug in J=x, K=2x, L=2x%2B10,and M=3x-5



8x%2B5=360 Combine like terms on the left side


8x=360-5Subtract 5 from both sides


8x=355 Combine like terms on the right side


x=%28355%29%2F%288%29 Divide both sides by 8 to isolate x



x=355%2F8 Reduce



Since x=355%2F8 (which is x=44.375 in decimal form), our first angle is J=44.375



Since x=44.375, we can plug this into K=2x to get

K=2%2844.375%29=88.75

So our second angle is K=88.75



Since x=44.375, we can plug this into L=2x%2B10 to get

L=2%2844.375%29%2B10=88.75%2B10=98.75

So our third angle is L=98.75


Since x=44.375, we can plug this into M=3x-5 to get

M=3%2844.375%29-5=133.125-5=128.125

So our fourth angle is M=128.125

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Answer:


So the measures of the four angles are:


J=44.375, K=88.75, L=98.75, and M=128.125



Check:

J%2BK%2BL%2BM=360 Start with the given equation

44.375%2B88.75%2B98.75%2B128.125=360 Plug in J=44.375, K=88.75, L=98.75, and M=128.125

360=360 Add. Since the two sides of the equation are equal, this verifies our answer.