Question 221519
The second angle of a triangle is 4 times as large as the first. The third angle is 120° more than the sum of the other two angles. Find the measure of the second angle.


Step 1.  Three angles of a triangle add up to 180 degrees.


Step 2.  Let x be the first angle.


Step 3.  Let 4x be the second angle since it's 4 times as large as the first.


Step 4.  Let x+4x=5x be the sum of the first and second angles.


Step 5.  Let 5x+120 be the third angle since it's 120 degrees more than the sum of the other two angles.


Step 6.  Then, x+4x+5x+120=180 since the three angles add up to 180


Step 7.  Solving the equation in Step 6 yields the following steps


*[invoke explain_simplification "x+4x+5x+120=180" ]


With x=6, then 4x=24 and 5x+120=150.  Note these angles add up to 180 degrees.


Step 8.  ANSWER:  The three angles are 6 degrees, 24 degrees and 150 degrees.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.