SOLUTION: The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.

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Question 213461: The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The second angle of a triangular kite is four times as large as the first. The third angle is 5 more than the sum of the other two angles. Find the measure of the second angle.

Step 1. Let a be the first angle, 4a is the second angle, and 5+a+4a=5+5a be the third angle where a+5a=5a is the sum of the other two angles

Step 2. Sum of the angles of a triangle is equal to 180. So

a%2B4a%2B5%2B5a=180

The following steps solve the above equation.

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


YOUR ANSWER


  • This is an equation! Solutions: a=17.5.
  • Graphical form: Equation a%2B4a%2B5%2B5a=180 was fully solved.
  • Text form: a+4a+5+5a=180 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+a%2B4a%2B5%2B5a=180+%29
    For tutors: simplify_cartoon( a+4a+5+5a=180 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at a%2B4%2Aa%2Bhighlight_red%28+5+%29%2B5%2Aa=180.
Moved 5 to the right of expression
It becomes a%2B4%2Aa%2B5%2Aa%2Bhighlight_green%28+5+%29=180.
Look at highlight_red%28+a+%29%2Bhighlight_red%28+4%2Aa+%29%2Bhighlight_red%28+5%2Aa+%29%2B5=180.
Eliminated similar terms highlight_red%28+a+%29,highlight_red%28+4%2Aa+%29,highlight_red%28+5%2Aa+%29 replacing them with highlight_green%28+%281%2B4%2B5%29%2Aa+%29
It becomes highlight_green%28+%281%2B4%2B5%29%2Aa+%29%2B5=180.
Look at %28highlight_red%28+1+%29%2Bhighlight_red%28+4+%29%2Bhighlight_red%28+5+%29%29%2Aa%2B5=180.
Added fractions or integers together
It becomes %28highlight_green%28+10+%29%29%2Aa%2B5=180.
Look at highlight_red%28+%28highlight_red%28+10+%29%29%2Aa+%29%2B5=180.
Remove unneeded parentheses around factor highlight_red%28+10+%29
It becomes highlight_green%28+10+%29%2Aa%2B5=180.
Look at 10%2Aa%2B5=highlight_red%28+180+%29.
Moved these terms to the left highlight_green%28+-180+%29
It becomes 10%2Aa%2B5-highlight_green%28+180+%29=0.
Look at 10%2Aa%2Bhighlight_red%28+5+%29-highlight_red%28+180+%29=0.
Added fractions or integers together
It becomes 10%2Aa%2Bhighlight_green%28+-175+%29=0.
Look at 10%2Aa%2Bhighlight_red%28+-175+%29=0.
Removed extra sign in front of -175
It becomes 10%2Aa-highlight_green%28+175+%29=0.
Look at highlight_red%28+10%2Aa-175+%29=0.
Solved linear equation highlight_red%28+10%2Aa-175=0+%29 equivalent to 10*a-175 =0
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: a=17.5.

Universal Simplifier and Solver


Done!




I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J