Let's analyze the problem from the image.

Given:

• In the left triangle: Two angles are $42^\circ$ and $85^\circ$.
• In the right triangle: One angle is $88^\circ$.
• We need to determine the value of $w^\circ$.

Step-by-Step Solution:

1. Find the third angle in the left triangle: Using the angle sum property of a triangle, the sum of angles in a triangle is always $180^\circ$. $42^\circ + 85^\circ + \text{Third Angle} = 180^\circ$ $\text{Third Angle} = 180^\circ - (42^\circ + 85^\circ) = 53^\circ$ Thus, the angle adjacent to $w^\circ$ is $53^\circ$.

2. Find the third angle in the right triangle: Similarly, apply the angle sum property for the right triangle. $88^\circ + y^\circ + x^\circ = 180^\circ$ However, we don’t need the exact values of $x^\circ$ or $y^\circ$ for now, as we will focus only on angles relevant to $w^\circ$.

3. Recognize the linear pair involving $w^\circ$: Since the angles $53^\circ$ and $w^\circ$ lie along a straight line (they are supplementary): $w^\circ + 53^\circ = 180^\circ$ $w^\circ = 180^\circ - 53^\circ = 127^\circ$

Final Answer:

$\boxed{127^\circ}$

Thus, the correct option is:

• C) 127°

Would you like further clarification or a detailed discussion about this solution?

Here are five related questions to expand your understanding:

1. What is the angle sum property of a triangle?
2. How do we identify supplementary angles?
3. What is the difference between adjacent and vertically opposite angles?
4. Why is the straight line property important in solving problems like this?
5. Can a triangle have two obtuse angles? Why or why not?

Tip: Always look for linear pairs when two lines intersect—they often help solve for unknown angles quickly.