To solve this problem, we are given the equation $m\angle WXY = 160^\circ$ and two unknowns $m\angle WXZ$ and $m\angle ZXY$. The angle expressions for these unknowns are given as:

• $m\angle WXZ = (5x + 8)^\circ$
• $m\angle ZXY = (7x - 4)^\circ$

We know that the sum of these two angles must equal 160° because:

$m\angle WXY = m\angle WXZ + m\angle ZXY$

So, the equation becomes:

$(5x + 8) + (7x - 4) = 160$

Let's solve this equation step by step:

1. Combine like terms:

$5x + 7x + 8 - 4 = 160$

$12x + 4 = 160$

2. Subtract 4 from both sides:

$12x = 156$

3. Divide by 12:

$x = 13$

Now that we know $x = 13$, we can substitute this value back into the expressions for $m\angle WXZ$ and $m\angle ZXY$.

• $m\angle WXZ = 5(13) + 8 = 65 + 8 = 73^\circ$
• $m\angle ZXY = 7(13) - 4 = 91 - 4 = 87^\circ$

Therefore:

• $m\angle WXZ = 73^\circ$
• $m\angle ZXY = 87^\circ$

The correct answer is the first option:

$\boxed{73^\circ, 87^\circ}$

Would you like more details on any part of the solution?

Here are 5 questions to expand your understanding:

1. What is the sum of the interior angles of a triangle?
2. How do you solve linear equations with variables on both sides?
3. How can you verify if two angles are supplementary?
4. What is the process for simplifying algebraic expressions?
5. How does substitution help solve systems of equations?

Tip: When solving for variables, always double-check your solutions by substituting the value back into the original expressions.