Explanation:
We are given six polygons, each with some interior angles labeled (in degrees), and we need to find the missing angle *x* in each case. To do this, we use the formula for the
sum of interior angles of a polygon:
> Sum = (n − 2) × 180°
where *n* is the number of sides.
Then, subtract the known angles from that sum to find *x*.
Let’s go one by one.
---
1) Pentagon (5 sides)
Sum = (5 − 2) × 180 = 3 × 180 =
540°
Given angles: 110°, 120°, 100°, 130°
Add them: 110 + 120 = 230; 230 + 100 = 330; 330 + 130 =
460
So x = 540 − 460 =
80°
✔ Check: 110 + 120 + 100 + 130 + 80 = 540 ✔️
---
2) Hexagon (6 sides)
Sum = (6 − 2) × 180 = 4 × 180 =
720°
Given angles: 120°, 110°, 130°, 120°, 110°
Add: 120 + 110 = 230; +130 = 360; +120 = 480; +110 =
590
x = 720 − 590 =
130°
✔ Check: 120+110+130+120+110+130 = 720 ✔️
---
3) Pentagon (5 sides) again → sum = 540°
Given: 105°, 115°, 120°, 100°
Sum of known: 105 + 115 = 220; +120 = 340; +100 =
440
x = 540 − 440 =
100°
✔ Check: 105+115+120+100+100 = 540 ✔️
---
4) Quadrilateral (4 sides)
Sum = (4 − 2) × 180 = 2 × 180 =
360°
Given: 95°, 100°, 110°
Sum known: 95 + 100 = 195; +110 =
305
x = 360 − 305 =
55°
✔ Check: 95+100+110+55 = 360 ✔️
---
5) Hexagon (6 sides) → sum = 720°
Given: 125°, 115°, 130°, 120°, 110°
Add: 125 + 115 = 240; +130 = 370; +120 = 490; +110 =
600
x = 720 − 600 =
120°
✔ Check: 125+115+130+120+110+120 = 720 ✔️
---
6) Triangle (3 sides)
Sum = (3 − 2) × 180 = 1 × 180 =
180°
Given: 50°, 60°
x = 180 − (50 + 60) = 180 − 110 =
70°
✔ Check: 50 + 60 + 70 = 180 ✔️
All calculations double-checked.
Final Answer:
1) 80°
2) 130°
3) 100°
4) 55°
5) 120°
6) 70°
Parent Tip: Review the logic above to help your child master the concept of interior angle worksheet.
