The image provided shows a geometry problem involving a diagram with angles. Here's a breakdown of what I see:

• The angle ∠PEC is given as $36^\circ$.
• An expression $5x + 17^\circ$ is also associated with an arc, likely representing the measure of an angle or arc on the circle.
• Another angle or arc measure is labeled as $128^\circ$.
• The diagram includes four possible equations to solve for $x$:
  • $22x - 36 = 128$
  • $5x - 19 = 128$
  • $22x + 36 = 128$
  • $5x + 53 = 128$

The problem asks which equation can be used to solve for $x$.

Approach:

Given that the angles and arcs are part of a circle, the equation likely relates to the properties of inscribed angles or the sum of angles along a straight line. Without further details, it seems that the relationship between the given angles, the arc, and the expression $5x + 17$ would help form an equation. The goal is to find the correct equation from the options that matches the geometry of the problem.

Solution:

Since the sum of angles forming a straight line should equal $180^\circ$, and the angle $36^\circ$ is given, the arc measure $128^\circ$ might be involved in this reasoning.

The most likely correct equation is: $5x + 17 = 128$

Rewriting this gives: $5x = 128 - 17$ $5x = 111$ Thus: $x = \frac{111}{5} = 22.2$

Would you like more details on the geometric reasoning or further explanations?

Related Questions:

1. How are angles and arcs related in a circle?
2. What is the relationship between inscribed angles and the arc they subtend?
3. How do we use the sum of angles on a straight line in circle geometry?
4. What are the different types of angles formed in a circle?
5. How can we use algebra to solve geometric problems involving expressions?

Tip:

When solving geometric problems with expressions, always focus on identifying key relationships between angles, arcs, and lines to form accurate equations.