In circle $A, \mathrm{mCB}=100^{\circ}$. Solve for $x$ if $\mathrm{m} \angle C A B=(7 x-50)^{\circ}$. If necessary, round your answer to the nearest tenth. B

Step 1 ：The problem involves a circle and angles. From the problem, we know that the measure of angle CB is 100 degrees and the measure of angle CAB is given by the expression \((7x - 50)\) degrees.

Step 2 ：In a circle, the angle subtended by an arc at the center is twice the angle subtended by it at any point on the alternate segment. This is known as the Inscribed Angle Theorem or the Angle at the Center Theorem.

Step 3 ：Therefore, we can set up the equation \(2*(7x - 50) = 100\) to solve for x.

Step 4 ：Solving the equation gives us \(x = \frac{100}{7}\). This is the value of x that makes the measure of angle CAB equal to half the measure of angle CB.

Step 5 ：Final Answer: \(x = \boxed{\frac{100}{7}}\)