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The image contains the following mathematical problem:

"Given that \( m \angle A = (13x)^\circ \), \( m \angle C = (7x + 35)^\circ \), and \( m \angle D = 125^\circ \), what is \( m \angle B \)?"

This appears to describe the angles of a quadrilateral, where the sum of the interior angles is always \( 360^\circ \). Let's solve this step by step.

### Step 1: Set up the equation for the sum of the angles in a quadrilateral.
For any quadrilateral, the sum of the interior angles is:
\[
m \angle A + m \angle B + m \angle C + m \angle D = 360^\circ
\]

Substitute the given expressions into this equation:
\[
(13x) + m \angle B + (7x + 35) + 125 = 360
\]

### Step 2: Simplify the equation.
First, combine the constants and terms involving \(x\):
\[
13x + 7x + 35 + 125 + m \angle B = 360
\]
\[
20x + 160 + m \angle B = 360
\]

### Step 3: Solve for \( m \angle B \).
Now, isolate \( m \angle B \) by subtracting \( 20x + 160 \) from both sides:
\[
m \angle B = 360 - 20x - 160
\]
\[
m \angle B = 200 - 20x
\]

This is the expression for \( m \angle B \).

### Conclusion:
The value of \( m \angle B \) is \( 200^\circ - 20x \). To find the specific value of \( m \angle B \), we would need the value of \(x\), which isn't directly given. But this is the general formula.

Let me know if you'd like further explanation or additional steps!

Here are 5 questions related to this problem:
1. How can we find the value of \(x\) in this scenario?
2. What would happen if this were not a quadrilateral?
3. Can this problem be extended to other polygons?
4. Why does the sum of angles in a quadrilateral always add up to 360°?
5. How could we approach solving for angles in a more complex polygon?

**Tip:** Always remember that the sum of interior angles of a polygon with \(n\) sides is \((n-2) \times 180^\circ\).

Given that m∠A = (13x)°, m∠C = (7x + 35)°, and m∠D = 125°, what is m∠B?

Learn how to solve for the missing angle m∠B in a quadrilateral where the sum of the interior angles equals 360°. Given expressions for angles m∠A = (13x)°, m∠C = (7x + 35)°, and m∠D = 125°, we calculate m∠B algebraically. This is suitable for students in Grades 8-10.

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