SOLUTION: IF THE MEASURES OF THE THREE ANGLES OF TRIANGLE ARE x, 2x - 20, and 3x - 10, then what is this type of traingle? Why?

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Question 215041This question is from textbook GEOMETRY
: IF THE MEASURES OF THE THREE ANGLES OF TRIANGLE ARE x, 2x - 20, and 3x - 10, then what is this type of traingle? Why? This question is from textbook GEOMETRY

Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
IF THE MEASURES OF THE THREE ANGLES OF TRIANGLE ARE x, 2x - 20, and 3x - 10, then what is this type of traingle? Why?

Step 1. The sum of the angles of a triangle add to 180 degrees.

Step 2. Then x+2x-20+3x-10=180.

Step 3. The following steps will solve the equation in step 2.

Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=35.
  • Graphical form: Equation x%2B2x-20%2B3x-10=180 was fully solved.
  • Text form: x+2x-20+3x-10=180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+x%2B2x-20%2B3x-10=180+%29
    For tutors: simplify_cartoon( x+2x-20+3x-10=180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at x%2B2%2Ax-highlight_red%28+20+%29%2B3%2Ax-highlight_red%28+10+%29=180.
Added fractions or integers together
It becomes x%2B2%2Ax%2Bhighlight_green%28+-30+%29%2B3%2Ax=180.
Look at x%2B2%2Ax%2Bhighlight_red%28+-30+%29%2B3%2Ax=180.
Moved -30 to the right of expression
It becomes x%2B2%2Ax%2B3%2Ax%2Bhighlight_green%28+-30+%29=180.
Look at x%2B2%2Ax%2B3%2Ax%2Bhighlight_red%28+-30+%29=180.
Removed extra sign in front of -30
It becomes x%2B2%2Ax%2B3%2Ax-highlight_green%28+30+%29=180.
Look at highlight_red%28+x+%29%2Bhighlight_red%28+2%2Ax+%29%2Bhighlight_red%28+3%2Ax+%29-30=180.
Eliminated similar terms highlight_red%28+x+%29,highlight_red%28+2%2Ax+%29,highlight_red%28+3%2Ax+%29 replacing them with highlight_green%28+%281%2B2%2B3%29%2Ax+%29
It becomes highlight_green%28+%281%2B2%2B3%29%2Ax+%29-30=180.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+2+%29%2Bhighlight_red%28+3+%29%29%2Ax-30=180.
Added fractions or integers together
It becomes %28highlight_green%28+6+%29%29%2Ax-30=180.
Look at highlight_red%28+%28highlight_red%28+6+%29%29%2Ax+%29-30=180.
Remove unneeded parentheses around factor highlight_red%28+6+%29
It becomes highlight_green%28+6+%29%2Ax-30=180.
Look at 6%2Ax-30=highlight_red%28+180+%29.
Moved these terms to the left highlight_green%28+-180+%29
It becomes 6%2Ax-30-highlight_green%28+180+%29=0.
Look at 6%2Ax-highlight_red%28+30+%29-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes 6%2Ax%2Bhighlight_green%28+-210+%29=0.
Look at 6%2Ax%2Bhighlight_red%28+-210+%29=0.
Removed extra sign in front of -210
It becomes 6%2Ax-highlight_green%28+210+%29=0.
Look at highlight_red%28+6%2Ax-210+%29=0.
Solved linear equation highlight_red%28+6%2Ax-210=0+%29 equivalent to 6*x-210 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=35.

Universal Simplifier and Solver


Done!



Step 4. With x=35, then 2x-20=70-20=50 and 3x-10=105-10=95.

Step 5. Since the triangle has angles 35, 50, and 95 where one angle is greater than 90 degrees then the triangle is an obtuse triangle by definition

I hope the above steps were helpful.

For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.

And good luck in your studies!

Respectfully,
Dr J