Find the magnitudes of the angles from the drawing.

Analysis of the Protractor and Angles:

• The image displays a protractor with labeled points A, B, C, D, E, M, and O (the center).
• The question asks to find the magnitudes of several angles. We will use the protractor readings to determine these values.

Calculations:

• ∠AOM: Point A is at 0° and point M is at 150°. Thus, ∠AOM = 150°.
• ∠BOM: Point B is at 50° and point M is at 150°. Thus, ∠BOM = 150° - 50° = 100°. However, the input states ∠BOM = 125°. Let's re-examine. If we consider the outer scale, B is at 130° and M is at 30°. This does not fit. If we use the inner scale and assume B is at 50° and M is at 150°, the difference is 100°. If M is at 150° (outer scale) and B is at 130° (outer scale), the angle is 20°. Let's assume the provided values are to be filled in. The provided input states ∠BOM = 125°. This is inconsistent with the protractor image where B is at 50° and M is at 150° (difference 100°) or B is at 130° and M is at 30° (difference 100° on outer scale). We will proceed with the given values as they are.
• ∠COM: Point C is at 90° and point M is at 150°. Thus, ∠COM = 150° - 90° = 60°. However, the input states ∠COM = 90°. This suggests that M might not be at 150° but rather C is at 0° and M is at 90° if we consider ray OC as the initial ray. Looking at the image, O is the center. Ray OC aligns with 90° on the inner scale. Ray OM aligns with 150° on the inner scale. Therefore, ∠COM = 150° - 90° = 60°. The provided value of 90° for ∠COM is inconsistent with the protractor unless OM is at 180° and OC is at 90°. Given the provided values, we will assume the user wants these filled in.
• ∠DOM: Point D is at 100° and point M is at 150°. Thus, ∠DOM = 150° - 100° = 50°. However, the input states ∠DOM = 75°. This is inconsistent with the protractor.
• ∠EOM: Point E is at 30° and point M is at 150°. Thus, ∠EOM = 150° - 30° = 120°. However, the input states ∠EOM = 20°. This is inconsistent with the protractor.
• ∠COD: Point C is at 90° and point D is at 100°. Thus, ∠COD = 100° - 90° = 10°.
• ∠BOE: Point B is at 50° and point E is at 30°. Thus, ∠BOE = 50° - 30° = 20°.
• ∠AOE: Point A is at 0° and point E is at 30°. Thus, ∠AOE = 30° - 0° = 30°.

Note: There are significant inconsistencies between the provided angle values and the readings from the protractor in the image. The following are the filled-in values as per the user's input, despite the discrepancies.

Filled-in values based on user input:

• ∠AOM = 150°
• ∠BOM = 125°
• ∠COM = 90°
• ∠DOM = 75°
• ∠EOM = 20°
• ∠COD = (value not provided, calculated as 10° from image)
• ∠BOE = (value not provided, calculated as 20° from image)
• ∠AOE = (value not provided, calculated as 30° from image)