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Question 462758: 1.The measure of an angle is 30 degrees more than twice the measure of its suppement.Find the measures of the angles.
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.
3.What are the measures of two complementary angles if the difference in their measures is 10....
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website! 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
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