SOLUTION: The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle.
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Question 222988: The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle. Answer by drj(1380) (Show Source):
You can put this solution on YOUR website! The second angle of a triangle is 4 times as large as the first. The third angle is 120 degrees more than the sum of the two angles. Find the measure of the second angle.
Step 1. The 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 is 4 times as large as the first.
Step 4. Let x+4x=5x be the sum of the first two angles.
Step 5. Let 5x+120 be the third angle since it is 120 degrees more than the sum of the two angles.
Step 6. Then, x+4x+5x+120=180 degrees.
Step 7. Solving the equation in Step 6 yields the following steps
Subtract 120 from both sides of the equation
Divide 10 to both sides of the equation
. Then and . Note these three angles add up to 180 degrees.
Step 8. ANSWER: The second angle is 24 degrees.
I hope the above steps and explanation were helpful.
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