We are given the following information from the diagram and question:

• $m\angle A = 16x$
• $m\angle C = 8x + 26^\circ$
• $m\angle D = 134^\circ$

We need to find $m\angle B$.

Since the angles $\angle A$, $\angle B$, $\angle C$, and $\angle D$ are part of a quadrilateral, the sum of the interior angles in a quadrilateral is always 360°.

So, the equation is:

$m\angle A + m\angle B + m\angle C + m\angle D = 360^\circ$

Substituting the given values:

$16x + m\angle B + (8x + 26^\circ) + 134^\circ = 360^\circ$

Now, let's simplify and solve this equation step by step.The expression for $m\angle B$ is:

$m\angle B = 200 - 24x$

To determine the exact value of $m\angle B$, we would need to know the value of $x$. Do you have more information on $x$, or would you like to proceed with further clarification?

Let me know if you'd like any details about this solution or have more questions. Here are 5 related questions:

1. How can we find the value of $x$ from the given information?
2. What is the general formula for the sum of angles in a polygon?
3. How do we apply algebraic substitution to find unknown angles?
4. What are some real-world applications of angle-sum properties in quadrilaterals?
5. Can this method be applied to non-convex quadrilaterals?

Tip: Always remember that the sum of the interior angles in any quadrilateral is 360°.