1. **Problem statement:** We are given that $\angle AFB$ and $\angle CFD$ are straight angles, and $\angle EFC$ is a right angle. We need to find the measure of $\angle CFB$. We are also given two angles expressed in terms of $x$: $3x^\circ$ and $(4x+13)^\circ$.\n\n2. **Understanding the angles:** \n- A straight angle measures 180°\n- A right angle measures 90°\n\n3. **Given information from the diagram:**\n- $\angle EFC = 90^\circ$ (right angle)\n- $\angle CFD = 180^\circ$ (straight angle)\n- $\angle AFB = 180^\circ$ (straight angle)\n- The angle between FE and FA is $3x^\circ$\n- The angle between FA and FD is $(4x+13)^\circ$\n\n4. **Find $x$:**\nSince $\angle EFC$ is 90°, and $\angle AFB$ and $\angle CFD$ are straight angles, the sum of angles around point F on the straight line C-F-D is 180°. The angles around F add up to 360°, so:\n\nThe sum of $3x^\circ$ and $(4x+13)^\circ$ plus the right angle 90° must equal 180° because they form a straight angle on one side:\n$$3x + (4x + 13) + 90 = 180$$\nSimplify:\n$$3x + 4x + 13 + 90 = 180$$\n$$7x + 103 = 180$$\nSubtract 103 from both sides:\n$$7x = 180 - 103$$\n$$7x = 77$$\nDivide both sides by 7:\n$$x = \cancel{\frac{7x}{7}} = \frac{77}{7} = 11$$\n\n5. **Find $m\angle CFB$:**\n$\angle CFB$ is the angle between rays CF and FB. Since $\angle CFD = 180^\circ$ and $\angle CFD = (4x + 13)^\circ + m\angle CFB$, we can write:\n$$m\angle CFB = 180 - (4x + 13)$$\nSubstitute $x = 11$:\n$$m\angle CFB = 180 - (4(11) + 13) = 180 - (44 + 13) = 180 - 57 = 123^\circ$$\n\n**Final answers:**\n- $x = 11$\n- $m\angle CFB = 123^\circ$