The sum of the measures of the interior angles in a triangle is $180^{\circ}$. The measure of the second angle is $52^{\circ}$ more than the measure of the first angle. The measure of the third angle is $47^{\circ}$ more than the measure of the first angle. Find the measure of the interior angles.

Step 1 ：The problem is asking for the measures of the interior angles of a triangle. We know that the sum of the measures of the interior angles in a triangle is \(180^{\circ}\). We also know that the measure of the second angle is \(52^{\circ}\) more than the measure of the first angle, and the measure of the third angle is \(47^{\circ}\) more than the measure of the first angle.

Step 2 ：We can set up an equation to represent this information and solve for the measure of the first angle. Once we have the measure of the first angle, we can easily find the measures of the second and third angles.

Step 3 ：Let's denote the measure of the first angle as \(x\). Then the measure of the second angle is \(x + 52^{\circ}\) and the measure of the third angle is \(x + 47^{\circ}\). The sum of the measures of the three angles is \(180^{\circ}\), so we have the equation \(x + (x + 52^{\circ}) + (x + 47^{\circ}) = 180^{\circ}\).

Step 4 ：We can solve this equation to find the value of \(x\).

Step 5 ：By solving the equation, we find that \(x = 27^{\circ}\).

Step 6 ：Substituting \(x = 27^{\circ}\) into the expressions for the second and third angles, we find that the second angle is \(79^{\circ}\) and the third angle is \(74^{\circ}\).

Step 7 ：Final Answer: The measures of the interior angles are \(\boxed{27^{\circ}}\), \(\boxed{79^{\circ}}\), and \(\boxed{74^{\circ}}\).