Question 12604
An angle and its compliment equal 90 degrees, an angle and its supplement equal 180 degrees, but using these two pieces of information we can solve your problem easily.
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Start by Defining your angles...
Let X be your Angle
90 - X is your complement
180 - X is your supplement
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Now we just need to write the equation
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{{{(1/2)(90-X)+(3/4)(180-X) = 110}}} Now we do Algebra
{{{ 45 - (X/2) + 135 - (3X/4) = 110 }}} combine like terms
{{{ 280 - ( 5X/4 ) = 110 }}} Subtract 280 from both sides
{{{ -(5X/4) = -170 }}} Multiply Both sides by {{{-(4/5) }}}
{{{ X = 136 }}} So our angle measure is 136 Degrees