From the image, the problem seems to involve geometry with points $A$, $Q$, $N$, and $P$ on a diagram, where lines and angles are involved. The task is to find the number of degrees in $\angle ANQ$, given some other angle values.

Based on what is visible from the image, here is the summarized problem:

• The figure shows points $A$, $N$, and $Q$ lying on the diagram.
• It is given that: $\angle QNP = 2x, \quad \angle ANP = 3x + 14$
• The goal is to find the value of $\angle ANQ$.

Solving the problem:

1. Since $\angle ANQ$ is part of the straight line, and the sum of angles around a point is $180^\circ$, we use: $\angle QNP + \angle ANP = 180^\circ$ Substituting the given values for the angles: $2x + (3x + 14) = 180$

2. Simplifying the equation: $5x + 14 = 180$ $5x = 166$ $x = 33.2$

3. Now that we know $x = 33.2$, we can substitute it back to find the value of $\angle ANP$ and $\angle QNP$:

   • $\angle QNP = 2x = 2(33.2) = 66.4^\circ$
   • $\angle ANP = 3x + 14 = 3(33.2) + 14 = 99.6 + 14 = 113.6^\circ$

4. Finally, to find $\angle ANQ$, we subtract $\angle QNP$ from $180^\circ$: $\angle ANQ = 180^\circ - 66.4^\circ = 113.6^\circ$

Thus, the measure of $\angle ANQ$ is 113.6°.

Would you like further details or clarifications on any part of the solution?

Here are some related questions you might want to explore:

1. How are angles around a point used in geometry?
2. What are supplementary angles, and how do they relate to this problem?
3. How do you solve linear equations involving angles?
4. What are different types of angles found in geometry (e.g., acute, obtuse)?
5. How does the concept of collinear points influence geometry problems?

Tip: In geometry, it's useful to remember that the sum of angles on a straight line is always 180°, which is a key tool for solving many angle-based problems.