SOLUTION: three angles of a triangle are in ratio 3:4:5. Find the measure of EACH angle

Question 837223: three angles of a triangle are in ratio 3:4:5. Find the measure of EACH angle
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sum of the angles of a triangle is 180 degrees.
the angles are in a ratio of 3:4:5.
if you allow the number of degrees in the first angles to be 3x, this means that the number of degrees in the second angle is equal to 4x and the number of degrees in the third angle is equal to 4x.
since the sum of the angles in a triangle is equal to 180 degrees, this means that:
3x + 4x + 5x = 180 degrees which means that 12x = 180.
divide both sides of this equation by 12 and you get x = 180 / 12 = 15 degrees.
this means that the 3x angles is equal to 45 degrees and the 4x angle is equal to 60 degrees and the 5x angle is equal to 75 degrees.
45 + 60 + 75 = 180 degrees so we're good there.
45 / 60 is equal to 3/4
60 / 75 is equal to 4/5
the angles are in the ratio of 3 to 4 to 5 which is as originally assumed, so we're good all around and that's your answer.
the angles are:
30, 45, 75
the ratio of 3:4:5 means that:
the first angle is in a ratio of 3/4 with the second angle.
the second angle is in a ratio of 4/5 with the third angle.
the first angle is in a ratio of 3/5 with the third angle.
the ratio of the first angle with the third angle is equal to 45/75.
simplify that by dividing both numerator and denominator by 15 and you get 3/5.
all the ratios hold true.

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