2) The measure of one angle of a triangle is twice the measure of another. The measure of

the third angle exceeds four times the measure of the smaller by 12 degrees. Find the

measure of each angle.

let A, B, C be angles of the triangle

A = 2B; so B = A/2

Therefore B is the smallest angle, so C = 4B + 12 = 2A + 12

now, A + B + C = 180, by angle sum property of a triangle

since we know that B = A/2 and C = 2A+12, lets substitute both of them in that equation.

A + A/2 + 2A + 12 = 180

(2A+A+4A+24) / 2 = 180

7A + 24 = 180 * 2

A = (360-24) / 7 = 48

Thus, B = A/2 = 48/2 = 24 and C = 4 (24) + 12 = 108.