The problem states that $m\angle 11 = x - 4$ and $m\angle 12 = 2x - 5$. We are given a diagram where $\angle 11$ and $\angle 12$ form a linear pair (they are supplementary). We need to find the value of $x$.

1. Problem Description

The problem states that $m\angle 11 = x - 4$ and $m\angle 12 = 2x - 5$. We are given a diagram where $\angle 11$ and $\angle 12$ form a linear pair (they are supplementary). We need to find the value of $x$.

2. Solution Steps

Since $\angle 11$ and $\angle 12$ form a linear pair, their measures add up to $180^\circ$.

$m\angle 11 + m\angle 12 = 180$

Substitute the given expressions for the measures of the angles:

$(x - 4) + (2x - 5) = 180$

Combine like terms:

$3x - 9 = 180$

Add 9 to both sides of the equation:

$3x = 189$

Divide both sides by 3:

$x = \frac{189}{3}$

$x = 63$

3. Final Answer

$x = 63$