Angles Around a Point Worksheets - Free Printable

It looks like you're referring to a worksheet titled "Angles around a Point", which asks you to find the measures of the unknown angles in each figure. Since I can't see the actual image, I’ll explain how to solve this type of problem and walk through the general method.

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🔷 Concept: Angles Around a Point

Key Rule:
The sum of all angles around a point is 360 degrees.

This means that if several angles meet at a single point (like rays or lines emanating from a common vertex), their total measure must add up to 360°.

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✔ Steps to Solve:

1. Identify all angles shown around the point.
2. Add up the known angles.
3. Subtract the sum of known angles from 360° to find the unknown angle(s).

> If there are multiple unknowns, and they are equal (e.g., marked with the same arc or labeled as congruent), divide the remaining degrees equally.

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📐 Example Problem (Hypothetical)

Suppose one diagram shows:
- Three angles: 100°, 120°, and an unknown angle $ x $, all meeting at a point.

Then:
$$
x = 360^\circ - (100^\circ + 120^\circ) = 360^\circ - 220^\circ = 140^\circ
$$

So, $ x = 140^\circ $

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💡 Common Patterns:

- If two angles are vertical angles, they are equal.
- If angles form a straight line, they sum to 180° (but only if it's a straight line — not relevant here unless specified).
- If multiple angles are marked the same, assume they are equal.

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🔍 Let’s Assume Your Worksheet Has These Types of Figures:

#### Figure A:
- Angles: 90°, 120°, 60°, and $ x $
- Sum of known: 90 + 120 + 60 = 270°
- $ x = 360 - 270 = 90^\circ $

#### Figure B:
- Angles: 80°, 100°, $ x $, $ x $ (two unknowns)
- Known sum: 80 + 100 = 180°
- Remaining: 360 - 180 = 180° → split between two equal angles
- $ x = 180 ÷ 2 = 90^\circ $

#### Figure C:
- Angles: 150°, $ x $, 70°, 60°
- Sum known: 150 + 70 + 60 = 280°
- $ x = 360 - 280 = 80^\circ $

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✔ Final Answer Format (for each figure):

Write the missing angle(s) based on the rule:
Sum of angles around a point = 360°

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If you can describe the figures or provide the angles shown in each diagram (e.g., "Figure 1 has angles 100°, 110°, and 70°, and one unknown"), I can give you exact answers for each.

Let me know what’s in the image!