It appears there is an error in the problem statement. The sum of the interior angles in a triangle is 180°, not 360°. Let's proceed with this correction.

The triangle has the following angles:

• One angle is $60^\circ$,
• Another angle is labeled $(c + 30)^\circ$,
• The third angle is $c^\circ$.

Using the fact that the sum of the angles in a triangle is $180^\circ$, we can write the equation:

$60^\circ + (c + 30)^\circ + c^\circ = 180^\circ$

Simplifying this equation:

$60 + c + 30 + c = 180$

$2c + 90 = 180$

Subtract 90 from both sides:

$2c = 90$

Divide by 2:

$c = 45$

Thus, the value of $c$ is $45^\circ$.

Would you like more details on this, or have any other questions?

Here are 5 related questions:

1. What would be the sum of angles if the triangle were an exterior angle sum problem?
2. How do we calculate exterior angles for polygons in general?
3. Can you explain the properties of different types of triangles (e.g., isosceles, equilateral)?
4. What is the relationship between an angle and its supplementary and complementary angles?
5. How do we apply the angle sum property to quadrilaterals and other polygons?

Tip: Always double-check whether a question is referring to interior or exterior angles. For triangles, the interior sum is always $180^\circ$, while exterior angles sum to $360^\circ$.