Concept:The exterior angle of a triangle is equal to the sum of its two opposite interior angles.The sum of all interior angles in a triangle is always 180 degrees.Explanation:We are given that one exterior angle of a triangle is $84°$.We are also told that the two interior opposite angles are in the ratio $1 : 2$.Let the two interior opposite angles be $x$ and $2x$.According to the property of exterior angles, the sum of these two interior opposite angles must be equal to the exterior angle.So, we can write the equation: $x + 2x = 84°$.Combining the terms, we get $3x = 84°$.To find the value of $x$, we divide $84°$ by $3$: $x = \frac{84°}{3} = 28°$.So, the first interior opposite angle is $x = 28°$.The second interior opposite angle is $2x = 2 \times 28° = 56°$.Now we have two angles of the triangle: $28°$ and $56°$.To find the third angle of the triangle, we use the fact that the sum of all interior angles in a triangle is $180°$.Let the third angle be $y$. Then, $28° + 56° + y = 180°$.Adding the known angles, we get $84° + y = 180°$.Subtracting $84°$ from both sides to find $y$: $y = 180° - 84° = 96°$.Therefore, the angles of the triangle are $28°$, $56°$, and $96°$.Answer:The angles of the triangle are 28°, 56°, 96°.