SOLUTION: angles PQR and ABC are supplementary, PQR is nine times larger than ABC determine the measures for each angle

Question 596747: angles PQR and ABC are supplementary, PQR is nine times larger than ABC determine the measures for each angle
Answer by math-vortex(648) (Show Source): You can put this solution on YOUR website!
Hi, there--
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Two angles are supplementary angles if the sum of their measures is 180 degrees.
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We need to write expressions for the two angles using algebra. Let's have x be the measure of angle ABC.
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In algebra, we write "nine times larger than ABC" as 9x. Thus the measure of angle PQR is 9x.
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We know that the sum of the measures of these two angles is 180, or
[measure of angle ABC] + [measure of angle PQR] = 180 degrees.
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Our equation is

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Combine like terms and solve for x.

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Divide both sides of the equation by 10 to isolate x.

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Our algebra steps show that the measure of angle ABC is x=18 degrees.
The measure of angle PQR is 9x=9*18=162 degrees.
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That's it. Feel free to email if you still have questions about this.
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Ms.Figgy
math.in.the.vortex@gmail.com
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