The problem is to find the value of angle $c$ in a triangle, given two other angles are $75^\circ$ and $71^\circ$.

1. Problem Description

The problem is to find the value of angle $c$ in a triangle, given two other angles are $75^\circ$ and $71^\circ$.

2. Solution Steps

The sum of the angles in a triangle is $180^\circ$.

Let the angles of the triangle be $A$, $B$, and $C$. We have $A = 75^\circ$, $B = 71^\circ$, and $C = 17c^\circ$.

However, from the diagram we understand that the question asks for the value of $c$ where the angle is $17c$ degrees.

The sum of the angles in a triangle is 180 degrees:

$A + B + C = 180$

Substituting the given values:

$75 + 71 + 17c = 180$

$146 + 17c = 180$

$17c = 180 - 146$

$17c = 34$

$c = \frac{34}{17}$

$c = 2$

3. Final Answer

2