# SOLUTION: 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.

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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.

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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

Solved by pluggable solver: EXPLAIN simplification of an expression

 Here's what you tried: This is an equation! Solutions: x=6. Graphical form: Equation was fully solved.Text form: x+4x+5x+120=180 simplifies to 0=0Cartoon (animation) form: For tutors: `simplify_cartoon( x+4x+5x+120=180 )` If you have a website, here's a link to this solution.

### DETAILED EXPLANATION

Look at .
Eliminated similar terms ,, replacing them with
It becomes .

Look at .
It becomes .

Look at .
Remove unneeded parentheses around factor
It becomes .

Look at .
Moved these terms to the left
It becomes .

Look at .
It becomes .

Look at .
It becomes .

Look at .
Solved linear equation equivalent to 10*x-60 =0
It becomes .
Result:
This is an equation! Solutions: x=6.

### Universal Simplifier and Solver

Done!

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.