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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!

One angle in a triangle has a measure that is three times as large as the smallest angle. The measure of the third angle is 45 degrees more than that of the smallest angle. Find the measure of the LARGEST angle.

Learn how to find the largest angle in a triangle where one angle is three times the smallest and another angle is 45 degrees more than the smallest. This problem involves algebra and geometry, suitable for Grades 6-8.

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