Find the missing angles in irregular polygons using the sum of interior angles formula.

A worksheet titled "Angles in Polygons" from Corbettmaths featuring six irregular polygons with given angles and one missing angle to find in each, labeled (a) through (f), with a play button and QR code for videos and examples.

PNG 1116×1010 59.3 KB Free · Personal Use

Quality Assured by Worksheets Library Team

Reviewed for educational accuracy and age-appropriateness

ID: #771637

✨ Generate New Worksheet

⭐

Show Answer Key & Explanations Step-by-step solution for: Angles in Polygons Textbook Exercise - Corbettmaths

▼

To solve for the missing angle `x` in each irregular polygon, we use the formula for the sum of interior angles of a polygon:

> Sum of interior angles = (n - 2) × 180°

where n is the number of sides.

Then, subtract the sum of the known angles from this total to find the missing angle `x`.

---

🔹 (a) Quadrilateral (4 sides)

- Sum of interior angles = (4 - 2) × 180° = 360°
- Known angles: 70°, 45°, 88°
- So, x = 360° - (70 + 45 + 88) = 360 - 203 = 157°

✔ Answer: x = 157°

---

🔹 (b) Pentagon (5 sides)

- Sum = (5 - 2) × 180° = 540°
- Known angles: 84°, 153°, 131°, 105°
- Sum of known = 84 + 153 + 131 + 105 = 473°
- x = 540 - 473 = 67°

✔ Answer: x = 67°

---

🔹 (c) Hexagon (6 sides)

- Sum = (6 - 2) × 180° = 720°
- Known angles: 120°, 130°, 100°, 135°, 110°
- Sum of known = 120 + 130 + 100 + 135 + 110 = 595°
- x = 720 - 595 = 125°

✔ Answer: x = 125°

---

🔹 (d) Pentagon (5 sides)

Note: There are three right angles (90°) shown with square symbols.

- Sum = (5 - 2) × 180° = 540°
- Known angles: 90°, 90°, 90°, 143°
- Sum of known = 90×3 + 143 = 270 + 143 = 413°
- x = 540 - 413 = 127°

✔ Answer: x = 127°

---

🔹 (e) Heptagon (7 sides)

- Sum = (7 - 2) × 180° = 900°
- Known angles: 96°, 105°, 161°, 123°, 155°, 114°
- Sum of known = 96 + 105 + 161 + 123 + 155 + 114
= Let’s add step by step:
- 96 + 105 = 201
- 201 + 161 = 362
- 362 + 123 = 485
- 485 + 155 = 640
- 640 + 114 = 754°
- x = 900 - 754 = 146°

✔ Answer: x = 146°

---

🔹 (f) Pentagon (5 sides)

- Sum = (5 - 2) × 180° = 540°
- Known angles: 150°, 127°, 202°, 40°
- Sum of known = 150 + 127 + 202 + 40 =
150 + 127 = 277
277 + 202 = 479
479 + 40 = 519°
- x = 540 - 519 = 21°

✔ Answer: x = 21°

---

## ✔ Final Answers:

| Part | Missing Angle x |
|------|------------------|
| (a) | 157° |
| (b) | 67° |
| (c) | 125° |
| (d) | 127° |
| (e) | 146° |
| (f) | 21° |

---

💡 Tip: Always count the number of sides first to know which formula to use. Then add up the known angles and subtract from the total sum to find the missing one. This works for any convex or concave polygon as long as you’re dealing with interior angles.

Parent Tip: Review the logic above to help your child master the concept of angles of a polygon worksheet.

Print Download