Angle Measure Overview, Finding & Estimation - Lesson | Study.com - Free Printable

To solve the problem, we need to determine the measures of the angles formed by the rays extending from point \( H \) to points \( D, C, E, F, \) and \( G \). The angle measures can be read directly from the protractor in the image.

Step-by-Step Solution:

1. Identify the Initial Ray:
- The initial ray is given as the positive \( x \)-axis, which is the horizontal line extending to the right from point \( H \).

2. Read the Angle Measures:
- The protractor is centered at point \( H \), and the angles are measured counterclockwise from the initial ray.

3. Measure Each Angle:
- Angle \( \angle DHF \):
- The ray \( HD \) points upward, and the protractor shows that the angle between \( HD \) and the initial ray is \( 90^\circ \).
- Therefore, \( \angle DHF = 90^\circ \).

- Angle \( \angle CHF \):
- The ray \( HC \) points slightly above the horizontal, and the protractor shows that the angle between \( HC \) and the initial ray is \( 45^\circ \).
- Therefore, \( \angle CHF = 45^\circ \).

- Angle \( \angle EHF \):
- The ray \( HE \) points to the left and slightly upward, and the protractor shows that the angle between \( HE \) and the initial ray is \( 135^\circ \).
- Therefore, \( \angle EHF = 135^\circ \).

- Angle \( \angle FHF \):
- The ray \( HF \) is the initial ray itself, so the angle between \( HF \) and the initial ray is \( 0^\circ \).
- Therefore, \( \angle FHF = 0^\circ \).

- Angle \( \angle GHF \):
- The ray \( HG \) points downward and to the left, and the protractor shows that the angle between \( HG \) and the initial ray is \( 225^\circ \).
- Therefore, \( \angle GHF = 225^\circ \).

Final Answer:

\[
\boxed{90^\circ, 45^\circ, 135^\circ, 0^\circ, 225^\circ}
\]