This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Step 1: Recall the definition of a straight angle. A straight angle is an angle that measures exactly . It forms a straight line.
Step 2: Relate the activity to the straight angle. The activity described (drawing a triangle, cutting out its angles, and joining them along a straight line) demonstrates that when the three interior angles of any triangle are placed adjacent to each other, they form a straight line.
Step 3: Conclude the sum of angles. Since the combined angles form a straight line, their sum must be equal to the measure of a straight angle. Therefore, the sum of the interior angles of a triangle is \boxed{*180^\circ*}}.
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Recall the definition of a straight angle. A straight angle is an angle that measures exactly 180^.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.