To find the value of \( x \), we can use the hint that the sum of the angle measures of a quadrilateral is \( 360^\circ \).
Let's define the angles in the quadrilateral based on the information you provided:
- One angle is \( (4x + 40)^\circ \).
- The second angle is \( 3x^\circ \).
Assuming there are two other angles (which are not specified), we can assume they are \( A \) and \( B \). However, since you only provided the expressions for two angles, let's set the sum of these two angles equal to \( 360^\circ \) first and solve for \( x \).
Let's assume the other two angles are zero or somehow not affecting the total for this current setting.
Now, we can write the equation:
\[ (4x + 40) + 3x = 360 \]
Combine like terms:
\[ 4x + 3x + 40 = 360 \]
This simplifies to:
\[ 7x + 40 = 360 \]
Now, subtract \( 40 \) from both sides:
\[ 7x = 360 - 40 \] \[ 7x = 320 \]
Now, divide by \( 7 \):
\[ x = \frac{320}{7} \]
Simplifying this gives:
\[ x \approx 45.71 \]
So, the value of \( x \) is:
\[ x \approx 45.71 \]
Make sure to clarify if there are other angles or if additional information was omitted to ensure full accuracy in solving the quadrilateral's angle measures.