The three angles of a triangle

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Question from Michelle, a student:

The second angle of a triangular garden is four times as large as the first.
The third angle is 45 less than the sum of the other two angles.
Find the measure of the other two angles?
My formula is x+4x+x+4x=180
10x-45=180
then subtract 45 from both sides and divide by 10
my answer 13.5 angle 1 54 angle 2 and 112.5 angle 3
however it looks backward to me but 13.5 + 67.5= 67.5 -112.5 would =45
less than the sum of the two angles.

Michelle,

There is a slip in line 4. You have x+4x+x+4x=180 but it should be x+4x+x+4x-45=180. You do however have it correctly on the next line

10x - 45 = 180.

Your error is in line 6. To solve the above equation you need to add 45 to each side to obtain

10x - 45 + 45 = 180 + 45

10x = 225.

Can you finish it now? Be sure to check your answer.

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.