The second angle of a triangle is three times as large as the first.  The third angle is 30 degrees more than the first.   Find the measure of each angle.   Give your answers from smallest to largest.  

Expert Answers

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In a triangle, all three angles must have a sum of 180 degrees.

In order to solve this problem, we will write each angle as an algebraic expression.  Since angle 2 and angle 3 are in relation to angle 1, we can say that:

`/_1=x` Since the 2nd angle is 3 times as large as first, we can say:

`/_2 = 3x` Since the 3rd angles is 30 more than the 1st, we can say:

`/_3 = x + 30` Since all 3 together must have sum of 180, we can say:

`(x) + (3x) + (x + 30) = 180` Solve for x

`5x +30 = 180` Subtract 30.

`5x = 150` Divide by 5.

`x = 30`

So the 1st angle is 30 degrees, the second angle is 90 degrees and the 3rd angle is 60 degrees.

Smallest = 1st angle of 30 degrees

Middle Angle = 3rd angle of 60 degrees

Largest angle = 2nd angle of 90 degrees

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