Question 462758
1.The measures of an angle is 30 degrees more than twice the measure of its suppement.Find the measures of the angles.
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I'll give you a step-by-step solution to problem #1 and problem #2. See if you can use it to solve #3 for yourself. You may send me a message if you have questions (address below.)
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An important part of solving these sorts of problems is being able to translate English sentences into mathematical equations. We start by assigning variables for the two angles.
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Let
x = the measure of the first angle
y = the measure of the second angle
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Reading the problem, we see that the measure of one angle is 30 degrees less than the measure of the other. Let's write that as an equation
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[measure of first angle] = [measure of second angle] - 30
x = y - 30
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We also see that the two angles are supplements. By definition, when two angles are supplementary, their measures add to 180 degrees. Let's write that as an equation.
[the measure of the first angle] + [the measure of the second angle] = 180
x + y = 180
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Now we have two equations in two variables , so we can solve for x and y. 
x = y - 30
x + y = 180
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Substitute y - 30 for x in the second equation, and solve for y.
x + y = 180
(y - 30) + y = 180
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Combine like terms
2y - 30 = 180
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Add 30 to both sides of the equation
2y = 180 + 30
2y = 210
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Divide both sides of the equation by 2
y = 210/2
y = 105
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The measure of the second angle is 105 degrees
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Substitute 105 for y in the first equation
x = y - 30
x = (105) - 30
x = 75
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The measure of the first angle is 75 degrees.
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Now, check your work.
(1) 105-75 = 30, so the first angle measures 30 degrees less than the second.
(2) 30+105 = 180, so the two angles are supplementary.
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2.Find the measures of two supplementary angles if the measure of one angle is 5 less than 4 times the measure of the other. 
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Let
x = the measure of the first angle
y = the measure of the second angle
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Reading the problem, we see that  the measure of one angle is 5 less than 4 times the measure of the other. Let's write that as an equation
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[measure of first angle] = [4 times][measure of second angle] - 5
x = 4y - 5
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We also see that the two angles are supplements. By definition, when two angles are supplementary, their measures add to 180 degrees. Let's write that as an equation.
[the measure of the first angle] + [the measure of the second angle] = 180
x + y = 180
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Now we have two equations in two variables , so we can solve for x and y. 
x = 4y - 5
x + y = 180
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Substitute 4y - 5 for x in the second equation, and solve for y.
x + y = 180
(4y - 5) + y = 180
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Combine like terms
5y - 5 = 180
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Add 5 to both sides of the equation
5y = 180 + 5
5y = 185
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Divide both sides of the equation by 5
y = 185/5
y = 37
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The measure of the second angle is 37 degrees
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Substitute 37 for y in the first equation
x = 4y - 5
x = 4(37) - 5
x = 148 - 5
x = 143
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The measure of the first angle is 143 degrees.
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Now, check your work.
(1) 4(37)-5 = 143, so the first angle measures 5 degrees less than four times the second.
(2) 37+143 = 180, so the two angles are supplementary.
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3.What are the measures of two complementary angles if the difference in their measures is 10.
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Now it's your turn. 
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FYI: If two angles are complementary, the sum of their measures is 90 degrees.
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hope this helps!
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Ms.Figgy
math.in.the.vortex@gmail.com