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.

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) (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,

Start with the given equation

Plug in , , ,and

Combine like terms on the left side

Subtract 5 from both sides

Combine like terms on the right side

Divide both sides by 8 to isolate x

Reduce

Since (which is in decimal form), our first angle is

Since , we can plug this into to get

So our second angle is

Since , we can plug this into to get

So our third angle is

Since , we can plug this into to get

So our fourth angle is

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Answer:

So the measures of the four angles are:

, , , and

Check:

Start with the given equation

Plug in , , , and

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