Geometry Worksheets | Angles Worksheets - Free Printable

Let's solve the problem step by step.

We are given two identical diagrams of a protractor with several rays extending from point A (the center) to points B, C, D, E, F on the edge of the semicircle. The goal is to find the measure of each angle in degrees:

- ∠CAB
- ∠DAB
- ∠EAB
- ∠CAF
- ∠DAF
- ∠EAF

We’ll use the protractor markings to determine the angles. The protractor is marked in degrees from 0° to 180°, with both inner and outer scales. Since the ray AB lies along the baseline (horizontal line), we can assume that AB is at 0° (or 180° depending on direction). But since the angles are measured from A, and the rays go upward into the semicircle, we'll use the outer scale for angles going clockwise from AB.

Let’s analyze the top diagram first.

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Step 1: Identify the positions of the points

From the diagram:
- Point B is at the left end (0° or 180°). Since the ray AB is horizontal and pointing left, it's aligned with 0° on the left side.
- Point F is at the right end, aligned with 180°.
- The protractor is labeled such that:
- The bottom scale goes from 0° (left) to 180° (right).
- So, we will read angles from AB (0°) to other points using the bottom scale.

Now, locate the rays:

#### Ray AC:
- Points to 150° on the protractor.
- So, ∠CAB = 150° – 0° = 150°

Wait — actually, we need to be careful. Let's look closely.

But wait — if AB is at 0° on the left, then moving clockwise to the right increases the angle.

So:
- AB → 0°
- AC → points to 150°? Wait — no. Looking at the image, C is near the 150° mark on the left side, but that’s the inner scale.

Wait — let's clarify the protractor orientation.

Typically:
- On a standard protractor:
- The bottom scale goes from 0° on the left to 180° on the right.
- The top scale goes from 180° on the left to 0° on the right.

But here, the ray AB is aligned with the left end, which is 0° on the bottom scale.

So:
- AB = 0°
- AF = 180°
- AD points to 120°
- AE points to 40°
- AC points to 160°

Wait — let’s double-check the markings.

Looking at the diagram:

- Point C is just before 170° on the left side, so around 160°
- Point D is at 120°
- Point E is at 40°
- Point F is at 180°

So, from point A:

- ∠CAB: from AB (0°) to AC (160°) → 160°
- ∠DAB: from AB (0°) to AD (120°) → 120°
- ∠EAB: from AB (0°) to AE (40°) → 40°
- ∠CAF: from AC (160°) to AF (180°) → 180° – 160° = 20°
- ∠DAF: from AD (120°) to AF (180°) → 180° – 120° = 60°
- ∠EAF: from AE (40°) to AF (180°) → 180° – 40° = 140°

Let’s confirm this with the second diagram — it looks identical.

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Final Answer:

Using the protractor readings:

| Angle | Measurement |
|-------|-------------|
| ∠CAB | 160° |
| ∠DAB | 120° |
| ∠EAB | 40° |
| ∠CAF | 20° |
| ∠DAF | 60° |
| ∠EAF | 140° |

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✔ Explanation:

- All angles are measured from point A.
- We use the bottom scale of the protractor since AB is at 0° and AF is at 180°.
- Each ray corresponds to a degree marking:
- AC → 160°
- AD → 120°
- AE → 40°
- To find angles between two rays, subtract the smaller degree from the larger one.

For example:
- ∠CAF = AF – AC = 180° – 160° = 20°
- ∠EAF = 180° – 40° = 140°

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✔ Final Answers:

Top Diagram:
- ∠CAB = 160°
- ∠DAB = 120°
- ∠EAB = 40°
- ∠CAF = 20°
- ∠DAF = 60°
- ∠EAF = 140°

Bottom Diagram: (Same as top)
- ∠CAB = 160°
- ∠DAB = 120°
- ∠EAB = 40°
- ∠CAF = 20°
- ∠DAF = 60°
- ∠EAF = 140°

✔ These are the correct measures based on the protractor readings.