Question

x 15 6x - 75 60°

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is $180^{\circ}$. So, we have the equation $(6x - 75)+60 + \text{third - angle}=180$. Since the third - angle is not given in terms of $x$ but we know that for a triangle with angles $A$, $B$, and $C$, $A + B + C=180^{\circ}$. Here, we assume the triangle is non - degenerate. If we consider the fact that we can also use the property for solving for $x$ in terms of the side - angle relationships. However, if we assume the triangle is equiangular (since one angle is $60^{\circ}$, and if it is equiangular all angles are $60^{\circ}$), we set $6x-75 = 60$.

Step2: Solve the equation for $x$

Add 75 to both sides of the equation $6x-75 = 60$. We get $6x=60 + 75$, so $6x=135$. Then divide both sides by 6: $x=\frac{135}{6}=22.5$. But if we assume the triangle is isosceles and the non - given angle is equal to the angle represented by $6x - 75$. Then $6x-75=60$.
Add 75 to both sides:
$6x=60 + 75$
$6x=135$
Divide both sides by 6:
$x = 25$
Since we assume the most straightforward case where we use the angle - sum property and the fact that one angle is $60^{\circ}$ and we try to find $x$ for the angle expression $6x - 75$.
$6x-75=60$
$6x=135$
$x = 25$

Answer:

$x = 25$