SOLUTION: If all angles in a triangle equal 180, and the largest angle measures 10 degrees less than the sum of the other two angles; and a different angle is the average of the other two, w

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Question 215469: If all angles in a triangle equal 180, and the largest angle measures 10 degrees less than the sum of the other two angles; and a different angle is the average of the other two, what are the measurements of all three angles?
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
If the sum of all angles in a triangle equal to 180, and the largest angle measures 10 degrees less than the sum of the other two angles; and a different angle is the average of the other two, what are the measurements of all three angles?

Step 1. Let x be one angle, y be the another angle

Step 2. Let x%2By-10 since the largest angle measures 10 degrees less than the sum of the other two angles.

Step 3. Let x=%28y%2Bx%2By-10%29%2F2 since a different angle is the average of the other two. Note the largest angle is included in the average. So if we solve for x then the other angle is y is added to the largest angle when conducting the average. Simplifying yields 2x=2y%2Bx-10 or x-2y=-10

Step 4. x%2By%2Bx%2By-10=180 or 2x%2B2y=190 since adding the three angles equals to 180

Step 5. Solve the system of equations shown below using substitution

x-2y=-10
2x%2B2y=190

Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++1%5Cx+%2B+-2%5Cy+=+-10%2C%0D%0A++++2%5Cx+%2B+2%5Cy+=+190+%29%0D%0A++We'll use substitution. After moving -2*y to the right, we get:
1%2Ax+=+-10+-+-2%2Ay, or x+=+-10%2F1+-+-2%2Ay%2F1. Substitute that
into another equation:
2%2A%28-10%2F1+-+-2%2Ay%2F1%29+%2B+2%5Cy+=+190 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101


With x=60 and y=35 then 180-35-60=85.

Now check for consistency.

85=x+y-10=60+35-10 for the largest triangle which is a true statement

x=60=(35+60)/2 which is also a true statement.

Step 6. The three angles are 35, 60, and 85 degrees

I hope the above steps were helpful.

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Good luck in your studies!

Respectfully,
Dr J