The total of all the angles in a triangle is equal to 180 degrees. Now we are given that in the particular triangle the largest angle is 6 times as large as the smallest and the third angle is 30 degrees more than the smallest.
Let the smallest angle by A, the largest angle is equal to 6A and the third angle is equal to A+ 30
A + 6A + A + 30 = 180
=> 8A + 30 = 180
=> 8A = 180 – 30
=> 8A = 150
=> A = 150/8
=> A = 18.75
Therefore the angles are 18.75, 112.5 and 48.75 degrees.
The required angles of the triangle are 18.75 degrees, 112.5 degrees and 48.75 degrees.
The smallest angle of the triangle is assumed to be x.
Since largest angle is 6 times the smallest angle, the largest angle = 6x.
The other angle is greater than the smallest bt 30 degree. So the other angle has to be x+3 dgree.
The therefore , the sum of the 3 angles = x+6x+x+30 = 8x+30.
Also the sum of the 3 angles of the is 180 degree. Therefore 8x+30 = 180 deg.
So 8x = 180-30 = 150.
Therefore x = 150/8 = 18.5 deg is the smallest angle.
The largest = 18.75/6 = 112.5 deg.
The 3rd angle = x+30 = 18.75+30 = 48.55 deg.