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Question 462566: ∠PQR and ∠ABC are complementary angles and ∠PQR is four times as large as ∠ABC. Determine the measure of each angle.
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! ∠PQR and ∠ABC are complementary angles and ∠PQR is four times as large as ∠ABC. Determine the measure of each angle.
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A big part of solving this problem is knowing how to translate an English sentence in to algebraic language.
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Let
x = the measure of ∠PQR
y = the measure of ∠ABC
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We know that the two angles are complementary. By definition, the sum of their measures is 90 degrees. We can write this as an equation:
[the measure of ∠PQR] + [the measure of ∠ABC] = 90 degrees
x + y = 90
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We also know that ∠PQR is four times as large as ∠ABC. Let's translate this into algebraic equation.
[the measure of ∠PQR] = 4 * [the measure of ∠ABC]
y = 4 * x
y = 4x
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Now we have two equations in two variables. Let's solve for x and y.
x + y = 90
y = 4x
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Substitute 4x for y in the first equation, and solve for x.
x + y = 90
x + (4x) = 90
5x = 90
x = 18
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Substitute 18 for x in the second equation, and solve for y.
y = 4x
y = 4(18)
y = 72
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We see that the measure of ∠PQR is 18 degrees and and the measure of ∠ABC is 72 degrees.
18 + 72 = 90, so the two angles are complementary.
72 = 4(18), so ∠PQR is four times as large as ∠ABC.
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hope this helps!
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Ms.Figgy
math.in.the.vortex
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