triangle angle sum problem

1. Identify the geometric principle: The sum of the interior angles of any triangle is always $180^{\circ}$.

2. Set up the equation: Based on the image, the three interior angles are $(3x + 15)^{\circ}$, $(4x - 12)^{\circ}$, and $79^{\circ}$. Therefore, we can write the equation:
$$(3x + 15) + (4x - 12) + 79 = 180$$

3. Combine like terms: Group the $x$ terms and the constant terms together:
$$(3x + 4x) + (15 - 12 + 79) = 180$$
$$7x + 82 = 180$$

4. Solve for x: Subtract 82 from both sides of the equation:
$$7x = 180 - 82$$
$$7x = 98$$
Now, divide by 7:
$$x = \frac{98}{7}$$
$$x = 14$$