document.write( "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.\r
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document.write( "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.\r
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document.write( "3.What are the measures of two complementary angles if the difference in their measures is 10.... \n" );
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Algebra.Com's Answer #317184 by math-vortex(648)![]() ![]() 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. \n" ); document.write( "============================================= \n" ); document.write( ". \n" ); document.write( "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.) \n" ); document.write( ". \n" ); document.write( "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. \n" ); document.write( ". \n" ); document.write( "Let \n" ); document.write( "x = the measure of the first angle \n" ); document.write( "y = the measure of the second angle \n" ); document.write( ". \n" ); document.write( "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 \n" ); document.write( ". \n" ); document.write( "[measure of first angle] = [measure of second angle] - 30 \n" ); document.write( "x = y - 30 \n" ); document.write( ". \n" ); document.write( "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. \n" ); document.write( "[the measure of the first angle] + [the measure of the second angle] = 180 \n" ); document.write( "x + y = 180 \n" ); document.write( ". \n" ); document.write( "Now we have two equations in two variables , so we can solve for x and y. \n" ); document.write( "x = y - 30 \n" ); document.write( "x + y = 180 \n" ); document.write( ". \n" ); document.write( "Substitute y - 30 for x in the second equation, and solve for y. \n" ); document.write( "x + y = 180 \n" ); document.write( "(y - 30) + y = 180 \n" ); document.write( ". \n" ); document.write( "Combine like terms \n" ); document.write( "2y - 30 = 180 \n" ); document.write( ". \n" ); document.write( "Add 30 to both sides of the equation \n" ); document.write( "2y = 180 + 30 \n" ); document.write( "2y = 210 \n" ); document.write( ". \n" ); document.write( "Divide both sides of the equation by 2 \n" ); document.write( "y = 210/2 \n" ); document.write( "y = 105 \n" ); document.write( ". \n" ); document.write( "The measure of the second angle is 105 degrees \n" ); document.write( ". \n" ); document.write( "Substitute 105 for y in the first equation \n" ); document.write( "x = y - 30 \n" ); document.write( "x = (105) - 30 \n" ); document.write( "x = 75 \n" ); document.write( ". \n" ); document.write( "The measure of the first angle is 75 degrees. \n" ); document.write( ". \n" ); document.write( "Now, check your work. \n" ); document.write( "(1) 105-75 = 30, so the first angle measures 30 degrees less than the second. \n" ); document.write( "(2) 30+105 = 180, so the two angles are supplementary. \n" ); document.write( ". \n" ); document.write( ". \n" ); document.write( "============================================= \n" ); document.write( "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. \n" ); document.write( "============================================= \n" ); document.write( ". \n" ); document.write( "Let \n" ); document.write( "x = the measure of the first angle \n" ); document.write( "y = the measure of the second angle \n" ); document.write( ". \n" ); document.write( "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 \n" ); document.write( ". \n" ); document.write( "[measure of first angle] = [4 times][measure of second angle] - 5 \n" ); document.write( "x = 4y - 5 \n" ); document.write( ". \n" ); document.write( "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. \n" ); document.write( "[the measure of the first angle] + [the measure of the second angle] = 180 \n" ); document.write( "x + y = 180 \n" ); document.write( ". \n" ); document.write( "Now we have two equations in two variables , so we can solve for x and y. \n" ); document.write( "x = 4y - 5 \n" ); document.write( "x + y = 180 \n" ); document.write( ". \n" ); document.write( "Substitute 4y - 5 for x in the second equation, and solve for y. \n" ); document.write( "x + y = 180 \n" ); document.write( "(4y - 5) + y = 180 \n" ); document.write( ". \n" ); document.write( "Combine like terms \n" ); document.write( "5y - 5 = 180 \n" ); document.write( ". \n" ); document.write( "Add 5 to both sides of the equation \n" ); document.write( "5y = 180 + 5 \n" ); document.write( "5y = 185 \n" ); document.write( ". \n" ); document.write( "Divide both sides of the equation by 5 \n" ); document.write( "y = 185/5 \n" ); document.write( "y = 37 \n" ); document.write( ". \n" ); document.write( "The measure of the second angle is 37 degrees \n" ); document.write( ". \n" ); document.write( "Substitute 37 for y in the first equation \n" ); document.write( "x = 4y - 5 \n" ); document.write( "x = 4(37) - 5 \n" ); document.write( "x = 148 - 5 \n" ); document.write( "x = 143 \n" ); document.write( ". \n" ); document.write( "The measure of the first angle is 143 degrees. \n" ); document.write( ". \n" ); document.write( "Now, check your work. \n" ); document.write( "(1) 4(37)-5 = 143, so the first angle measures 5 degrees less than four times the second. \n" ); document.write( "(2) 37+143 = 180, so the two angles are supplementary. \n" ); document.write( ". \n" ); document.write( ". \n" ); document.write( "============================================= \n" ); document.write( "3.What are the measures of two complementary angles if the difference in their measures is 10. \n" ); document.write( "============================================= \n" ); document.write( ". \n" ); document.write( "Now it's your turn. \n" ); document.write( ". \n" ); document.write( "FYI: If two angles are complementary, the sum of their measures is 90 degrees. \n" ); document.write( ". \n" ); document.write( "hope this helps! \n" ); document.write( ". \n" ); document.write( "Ms.Figgy \n" ); document.write( "math.in.the.vortex@gmail.com \n" ); document.write( " |