Let the measure of the smallest angle in the triangle be denoted as $x$.

According to the problem:

• The second angle is three times as large as the smallest angle, so its measure is $3x$.
• The third angle is 25 degrees more than the smallest angle, so its measure is $x + 25^\circ$.

We know that the sum of the angles in any triangle is 180 degrees. Therefore, we can set up the following equation:

$x + 3x + (x + 25) = 180$

Now, solve for $x$:

$x + 3x + x + 25 = 180$ $5x + 25 = 180$ $5x = 180 - 25$ $5x = 155$ $x = \frac{155}{5} = 31$

Now that we know $x = 31^\circ$, we can find the measures of the other two angles:

• The second angle is $3x = 3 \times 31 = 93^\circ$.
• The third angle is $x + 25 = 31 + 25 = 56^\circ$.

The largest angle is the one with the measure of $93^\circ$.

Final Answer:

The measure of the largest angle is 93 degrees.

Would you like more details or have any questions? Here are some related questions you might find interesting:

1. How do you solve for angles in non-right triangles?
2. What is the relationship between the angles in an equilateral triangle?
3. How can you prove that the sum of angles in any triangle is always 180 degrees?
4. How would the solution change if one of the angles were 90 degrees?
5. What is the largest angle in a triangle with angles 45°, 45°, and 90°?

Tip: When working with angles in triangles, always remember that the sum of the interior angles is 180°. This is a crucial property for solving angle problems.