A triangle is such that the largest angle is three times the smallest angle The third angle is 9 degrees less than the largest angle Find the measure of each angle?

Answer 1

Answer: The measure of angles in degrees are : 81, 72, 27. Solution: suppose the angles of triangle are: x, y, z where x > y > z. given: x = 3 z ......................................................(1) y = x - 9 ....................................................(2) we have 3 unknowns (x, y, z) with only two equations, in this case there is no solution. So we have to think in additional related equation: there is a rule for the Sum of Angles Inside a Triangle: x + y + z = 180 .........................................(3) Now we can solve these three equations to obtanin x, y and z: from eq. (1): z = x/3 ......................................................(2`) substitute eq. (2) and eq. (2`) in eq. 3: x + (x-9) + x/3 = 180 multiply last equation by 3: 3 x +3x - 27 + x = 540 7 x - 27 = 540 add 27 to both sides: 7 x =567 divide both sides by 7: x = 567/7 x = 81. substitute in eq. (2) y = 81 - 9 y = 72.substitute in eq. (2`): z = 81/27 z = 27. so the measure of angles in degrees are : 81, 72, 27.