To find the value of x, the given angles are summed up and the expression is set equal to 180° to utilize the fact that the sum of angles in a triangle is 180°. After simplifying and solving the equation, the value of x is found to be approximately 6.09.
Step-by-step explanation:
The question requires solving for the variable x in a linear equation stemming from a geometry problem, likely related to the angles of a triangle.
Step 1: Start by adding the two known angles.
65° + 65° = 130°
Step 2: Use the sum of angles in a triangle (180°) to set up the equation with the given expression for the third angle.
130° + (11x - 17°) = 180°
Step 3: Solve for x by first combining like terms.
11x + 130° - 17° = 180°
11x + 113° = 180°
Step 4: Subtract 113° from both sides of the equation.
11x = 180° - 113°
11x = 67°
Step 5: Divide both sides by 11 to find x.
x = 67° / 11
x = 6.09
Thus, the value of x is approximately 6.09.