Question 158825
Hi, Hope I can help,
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Could you help with this problem? It is from a worksheet. 
The excess of an angle over its supplement is 20 degrees. Find the angle. 
I tried x/180-x = 20 It doesn' come out even.
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Supplementary angles always add up to 180 degrees
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first we have to find the variables of the angles
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The excess of an angle over its supplement is 20 degrees (excess means exceeding, or more than)
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One angles would be "x"
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The other angle ( The excess of an angle over its supplement is 20 degrees) is "x+20" ( This angle is 20 degrees more than the first angle "x")
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One angle = {{{ x }}} degrees
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The second angle = {{{ x + 20 }}} degrees
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Now just add the angles together (supplementary angles add up to 180 degrees
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The equation would be {{{ (x) + (x+20) = 180 }}}, now just solve for "x"
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{{{ (x) + (x+20) = 180 }}} = {{{ x + x + 20 = 180 }}}, add like terms
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{{{ x + x + 20 = 180 }}} = {{{ highlight(x) + highlight(x) + 20 = 180 }}} = {{{ 2x + 20 = 180 }}}
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Move "20" to the right side
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{{{ 2x + 20 = 180 }}} = {{{ 2x + 20 - 20 = 180 - 20 }}} = {{{ 2x = 160 }}}
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To solve for "x" we will divide each side by "2"
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{{{ 2x = 160 }}} = {{{ 2x/2 = 160/2 }}} = {{{ x = 80  }}}
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x = {{{ 80 }}}
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We can check by replacing "x" with "80" in our equation
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{{{ (x) + (x+20) = 180 }}} = {{{ (80) + ((80)+20) = 180 }}} = {{{ 80 + (100) = 180 }}} = {{{ 80 + 100 = 180 }}} = {{{ 180 = 180 }}} (True)
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x = {{{ 80 }}}
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Our two angle measurements were: (Replace "x" with "80" )
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One angle = {{{ x }}} degrees, {{{ 80 }}} degrees
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The second angle = {{{ x + 20 }}} degrees, {{{ 80+20 }}} degrees, {{{ 100 }}} degrees
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The two angles add up to 180 degrees, {{{ 80 + 100 = 180 }}} = {{{ 180 = 180 }}} (True)
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The two angles are:
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1. {{{ 80 }}} degrees
2. {{{ 100 }}} degrees, (the first angle's supplement)
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Hope I helped, Levi