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put this solution on YOUR website!Notice that angles LPS and MPS are supplementary because they add to form line LM.
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Therefore their measures add to 180 degrees. So we can write:
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LPS + MPS = 180
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But the problem says that the measure of angle LPS is 3x + 2y and the measure of angle MPS
is 3x - 2y. Substituting these two values into the above equation results in:
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3x + 2y + 3x - 2y = 180
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The two terms containing y are equal, but of opposite sign. Therefore, they cancel out or
combine to zero, and this leaves the equation:
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3x + 3x = 180
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Combining the two terms containing x results in:
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6x = 180
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and you can solve for x by dividing both sides by 6 to get:
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x = 180/6 = 30 degrees
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Now notice that the measures of angles RPL and LPS are supplementary because these angles
combine to form line RS. In equation form this becomes:
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RPL + LPS = 180
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But the problem tells you that the measure of RPL is x + y and the measure of LPS is
3x + 2y. Substituting these results in the equation becoming:
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x + y + 3x + 2y = 180
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Combining the x and y terms on the left side results in:
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4x + 3y = 180
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You have previously found that x = 30 degrees. Substitute this and you get:
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4*30 + 3y = 180
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Multiply the 4 times 30 to get 120 and the equation becomes:
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120 + 3y = 180
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Get rid of the 120 on the left side by subtracting 120 from both sides to simplify the
equation to:
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3y = 60
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Solve for y by dividing both sides of this equation by 3 to find that:
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y = 60/3 = 20 degrees.
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Now you have that x = 30 degrees and y = 20 degrees. All you need to do is to substitute
these values to find the angle measures:
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RPL = x + y = 30 + 20 = 50 degrees
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LPS = 3x + 2y = 3*30 + 2*20 = 90 + 40 = 130 degrees
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and
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MPS = 3x - 2y = 3*30 - 2*20 = 90 - 40 = 50
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Notice that RPL and MPS are opposite angles and they SHOULD therefore be equal as they
actually turn out to be.
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Hope this helps you to work your way through this problem ...
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