https://file.aiquickdraw.com/mathbot/file/1728002582862n8wx6mpj.jpg

We are given that \(\angle WZY = 140^\circ\) and need to find \(\angle WZX\). The problem shows that:

\[
\angle WZX = (8b + 49)^\circ \quad \text{and} \quad \angle XZY = (3b + 102)^\circ
\]

Using the **Angle Addition Postulate**, we know:

\[
\angle WZY = \angle WZX + \angle XZY
\]

Substitute the known expressions:

\[
140^\circ = (8b + 49)^\circ + (3b + 102)^\circ
\]

Now, simplify and solve for \(b\):

\[
140 = (8b + 49) + (3b + 102)
\]
\[
140 = 11b + 151
\]

Subtract 151 from both sides:

\[
140 - 151 = 11b
\]
\[
-11 = 11b
\]

Now, solve for \(b\):

\[
b = -1
\]

Now substitute \(b = -1\) back into the expression for \(\angle WZX\):

\[
\angle WZX = 8(-1) + 49 = -8 + 49 = 41^\circ
\]

Thus, \(\angle WZX = 41^\circ\).

Would you like further details or have any questions? 

Here are 5 related questions to deepen your understanding:
1. How does the Angle Addition Postulate help solve angle problems?
2. What happens if the angle sum exceeds \(180^\circ\) in this kind of diagram?
3. How would the problem change if \(\angle WZY\) were given as obtuse?
4. What would happen if \(b\) were positive? Does it affect the overall geometry?
5. Can you derive other equations for \(\angle WZY\) if the angles were described differently?

**Tip**: Always check your final result by substituting values back into the original equations to verify your solution!

Find ∠WZX if the measure of ∠WZY is 140°, where ∠WZX = (8b + 49)° and ∠XZY = (3b + 102)°.

In this problem, we solve for ∠WZX using the Angle Addition Postulate and algebraic equations. Given that ∠WZY is 140°, the solution involves combining the algebraic expressions for the angles ∠WZX and ∠XZY. This example is ideal 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