https://file.aiquickdraw.com/mathbot/file/1727366490390m0ct5eoj.jpg

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°.

Given that m∠A = (16x)°, m∠C = (8x + 26)°, and m∠D = 134°, what is m∠B?

Learn how to find an unknown angle in a quadrilateral when given expressions for three of its angles. This problem uses the angle sum property of quadrilaterals and algebraic equations to solve for the missing angle. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation