SOLUTION: ∠PQR and ∠ABC are supplementary angles and ∠PQR is nine times as large as ∠ABC. Determine the measure of each angle. Students must show all work step by ste

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Question 474211: ∠PQR and ∠ABC are supplementary angles and ∠PQR is nine times as large as ∠ABC. Determine the measure of each angle. Students must show all work step by step to receive full credit for the problem.
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
∠PQR and ∠ABC are supplementary angles and ∠PQR is nine times as large as ∠ABC. Determine the measure of each angle.
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Let angle PQR be "x"
Let angle ABC be "y"
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Equations:
x + y = 180 degrees
x = 9y
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Substitute for "x" and solve for "y":
9y + y 180
10y = 180
y = 18 degrees
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Solve for "x":
x + y = 180
x + 18 = 180
x = 162 degrees
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Cheers,
Stan H.
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Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Let represent the measure of . Then must represent the measure of . The sum of the measures of supplementary angles is . Hence:



Solve for , then calculate

John

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