Let's solve each part of
Question 1: *Find the missing angle in each irregular polygon.*
We'll use the formula for the
sum of interior angles of a polygon:
> Sum of interior angles = $(n - 2) \times 180^\circ$,
> where $n$ is the number of sides.
Then, subtract the known angles to find the missing one.
---
(a) Quadrilateral (4 sides)
- Angles: $70^\circ$, $x$, $88^\circ$, $45^\circ$
- Sum of interior angles = $(4 - 2) \times 180^\circ = 360^\circ$
$$
x = 360^\circ - (70 + 88 + 45) = 360 - 203 = 157^\circ
$$
✔ Answer: $x = 157^\circ$
---
(b) Pentagon (5 sides)
- Angles: $84^\circ$, $153^\circ$, $131^\circ$, $105^\circ$, $x$
- Sum = $(5 - 2) \times 180 = 540^\circ$
$$
x = 540 - (84 + 153 + 131 + 105) = 540 - 473 = 67^\circ
$$
✔ Answer: $x = 67^\circ$
---
(c) Hexagon (6 sides)
- Angles: $120^\circ$, $130^\circ$, $100^\circ$, $135^\circ$, $110^\circ$, $x$
- Sum = $(6 - 2) \times 180 = 720^\circ$
$$
x = 720 - (120 + 130 + 100 + 135 + 110) = 720 - 695 = 25^\circ
$$
✔ Answer: $x = 25^\circ$
---
(d) Pentagon (5 sides)
- Shape has 5 sides (one side curved? No — it's a pentagon with 5 vertices)
- Angles: three right angles ($90^\circ$), $143^\circ$, and $x$
- So angles: $90^\circ$, $90^\circ$, $90^\circ$, $143^\circ$, $x$
- Sum = $540^\circ$
$$
x = 540 - (90 + 90 + 90 + 143) = 540 - 413 = 127^\circ
$$
✔ Answer: $x = 127^\circ$
---
(e) Heptagon (7 sides)
- Angles: $96^\circ$, $105^\circ$, $161^\circ$, $123^\circ$, $155^\circ$, $114^\circ$, $x$
- Sum = $(7 - 2) \times 180 = 900^\circ$
Add known angles:
$$
96 + 105 = 201 \\
201 + 161 = 362 \\
362 + 123 = 485 \\
485 + 155 = 640 \\
640 + 114 = 754
$$
$$
x = 900 - 754 = 146^\circ
$$
✔ Answer: $x = 146^\circ$
---
(f) Pentagon (5 sides)
- Angles: $x$, $150^\circ$, $127^\circ$, $202^\circ$, $40^\circ$
- But wait — one angle is $202^\circ$? That’s greater than $180^\circ$, so it's a reflex angle. But we still count it as an interior angle.
Sum = $540^\circ$
$$
x = 540 - (150 + 127 + 202 + 40) = 540 - 519 = 21^\circ
$$
✔ Answer: $x = 21^\circ$
---
✔ Final Answers:
| Part | Missing Angle |
|------|----------------|
| (a) | $157^\circ$ |
| (b) | $67^\circ$ |
| (c) | $25^\circ$ |
| (d) | $127^\circ$ |
| (e) | $146^\circ$ |
| (f) | $21^\circ$ |
Let me know if you'd like a visual explanation or diagram breakdown!
Parent Tip: Review the logic above to help your child master the concept of angles of polygons worksheets.
