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# The sum

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The sum of the measures of the angles of a triangle is 180. The sum of the measures of the second and third angles is four times the measure of the first angle. The third angle is 12 more than the second. Let x, y, and z represent the measures of the first, second, and third angles, respectively. Find the measures of the three angles.

Mar 24, 2022

#1
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x + y + z  =  180

y + z  =  4x

z  =  12 + y

Combining the first and second equations:  x + 4x  =  180     --->     5x  =  180     --->     x  =  36

Replacing this value into the second equation:  y + z  =  4(36)     --->     y + z  = 144

Combining this with the third equation:

y + z  =  144

z  =  12 + y

--->     y + 12 + y  =  144

2y  =  132

y  =  61

--->     z  =  12 + y  =  12 + 61  =  73

But, this is impossible!  Where did I make my mistake?

Mar 24, 2022
#2
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< Where did I make my mistake? >

At   2y = 132    =>>    y = 61    simple arithmetic error

actually, half of 132 is 66

.

Mar 24, 2022