SOLUTION: Please help me solve this problem. {{{The measures of the angles of triangle ABC are 5x, 4x-1, and 3x+13. Find the measure of each angle of the triangle. Explain}}}

Algebra ->  Triangles -> SOLUTION: Please help me solve this problem. {{{The measures of the angles of triangle ABC are 5x, 4x-1, and 3x+13. Find the measure of each angle of the triangle. Explain}}}      Log On


   



Question 119671: Please help me solve this problem.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

If the angles in triangle ABC are A,B, and C, then:
the angle A+=+5x
the angle B+=+4x-1+ and
the angle C+=+3x%2B13
Since their sum is +180, we will have:
A+%2B+B+%2B+C+=+180……….substitute A,B, and C
5x+%2B+%284x-1+%29+%2B+%283x%2B13%29+=+180……….solve for x
5x+%2B+4x+-1+%2B+3x+%2B13+=+180……….
12x++%2B12+=+180……….
12x++=+180+-+12……….
12x++=+168……….
x++=+168%2F12……….
x++=+14……….
Now calculate each angle:
A+=+5x……………… substitute x+……….
A+=+5%2A14
A+=+70………… the angleA+


B+=+4%2A14+-+1+………….. substitute x+……….
B+=+56+-+1+
B+=+55…………….. the angleB+
C+=+3%2A14+%2B13……………… substitute x+……….
C+=+42+%2B13
C+=+55…………. the angleC+

Check their sum:
A+%2B+B+%2B+C+=+180……….
70+%2B+55+%2B+55+=+180……….
70+%2B+110+=+180……….
180+=+180……….