Find the angle of shaded portions in circles — a math worksheet for calculating degrees in circle segments.

Let’s solve each problem step by step.

We know that a full circle is 360 degrees.
Each circle is divided into equal parts (like slices of a pie).
To find the angle of the shaded portion, we:

1. Count how many total equal parts the circle is divided into.
2. Count how many of those parts are shaded.
3. Divide 360 by the total number of parts to get the size of one part.
4. Multiply that by the number of shaded parts.

Let’s go one by one.

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Problem 1:
Circle divided into 2 equal parts → each part = 360 ÷ 2 = 180°
Shaded: 1 part → 1 × 180 = 180°

Problem 2:
Divided into 4 parts → each = 360 ÷ 4 = 90°
Shaded: 3 parts → 3 × 90 = 270°

Problem 3:
Divided into 8 parts → each = 360 ÷ 8 = 45°
Shaded: 5 parts → 5 × 45 = 225°

Problem 4:
Divided into 3 parts → each = 360 ÷ 3 = 120°
Shaded: 1 part → 1 × 120 = 120°

Problem 5:
Divided into 6 parts → each = 360 ÷ 6 = 60°
Shaded: 2 parts → 2 × 60 = 120°

Problem 6:
Divided into 4 parts → each = 90°
Shaded: 3 parts → 3 × 90 = 270°

Problem 7:
Divided into 8 parts → each = 45°
Shaded: 2 parts → 2 × 45 = 90°

Problem 8:
Divided into 6 parts → each = 60°
Shaded: 4 parts → 4 × 60 = 240°

Problem 9:
Divided into 3 parts → each = 120°
Shaded: 2 parts → 2 × 120 = 240°

Problem 10:
Divided into 8 parts → each = 45°
Shaded: 5 parts → 5 × 45 = 225°

Problem 11:
Divided into 8 parts → each = 45°
Shaded: 6 parts → 6 × 45 = 270°

Problem 12:
Divided into 8 parts → each = 45°
Shaded: 5 parts → 5 × 45 = 225°

Problem 13:
Divided into 8 parts → each = 45°
Shaded: 5 parts → 5 × 45 = 225°

Problem 14:
Divided into 6 parts → each = 60°
Shaded: 1 part → 1 × 60 = 60°

Problem 15:
Divided into 8 parts → each = 45°
Shaded: 7 parts → 7 × 45 = 315°

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Final Answer:
1) 180
2) 270
3) 225
4) 120
5) 120
6) 270
7) 90
8) 240
9) 240
10) 225
11) 270
12) 225
13) 225
14) 60
15) 315