We can solve the problem using algebra.

Let the measure of the smallest angle be $x$.

• The second angle is three times the smallest, so it measures $3x$.
• The third angle is 45 degrees more than the smallest angle, so it measures $x + 45^\circ$.

In a triangle, the sum of the angles is always 180 degrees. Therefore, we can set up the equation:

$x + 3x + (x + 45^\circ) = 180^\circ$

Simplifying the equation:

$5x + 45^\circ = 180^\circ$

Subtract 45 degrees from both sides:

$5x = 135^\circ$

Now, solve for $x$:

$x = \frac{135^\circ}{5} = 27^\circ$

So, the smallest angle is $27^\circ$.

Now, we can find the other angles:

• The second angle is $3x = 3 \times 27^\circ = 81^\circ$.
• The third angle is $x + 45^\circ = 27^\circ + 45^\circ = 72^\circ$.

The largest angle is $81^\circ$.

Answer: The largest angle is 81 degrees.

Would you like further details or clarification on this? Here are five related questions to consider:

1. How do you calculate the sum of the interior angles for any polygon?
2. If one of the angles in a triangle is 90 degrees, how do you classify that triangle?
3. What happens to the angles of a triangle if one angle is doubled?
4. How can you use trigonometry to find unknown angles in a right triangle?
5. How does the exterior angle theorem apply to triangles?

Tip: Always remember that the sum of the interior angles of any triangle is 180 degrees!