Let the angles are x, y and z.
Let the smallest angle is x
one angle is 78 degrees more than the smallest angle.⇒ y = x + 78 → (1)
the third angle is 4 times as large as the smallest angle. ⇒ z = 4 x → (2)
we should know that the sum of the angles of the triangle = 180°
∴ x + y + z = 180 →(3)
substitute from (1) and (2) at (3)
∴ x + ( x +78) + (4x) = 180
∴ 6x = 180 - 78 = 102
∴ x = 102 ÷ 6 = 17°
∴ y = 17 + 78 = 95°
∴ z = 4x = 68°
So, the measures of all three angles are 17°, 95° and 68°
