Answer:
∠ABC = 120°
ΔABC = 16√3 cm²
Explanation:
Part (a)
Sum of interior angles of a regular polygon = (n - 2) × 180°
(where n is the number of sides)
⇒ Sum of interior angles of a regular hexagon = (6 - 2) × 180° = 720°
All the interior angles in a regular polygon are equal.
⇒ Interior angle = sum of interior angles ÷ number of sides
⇒ ∠ABC = 720° ÷ 6
⇒ ∠ABC = 120°
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Part (b)
Use the sine rule for area of a triangle:
![\frac12ab \sin(C)](https://img.qammunity.org/2023/formulas/mathematics/high-school/8zkk3vk0d2lmccgirnbwwxiyfkt7ud4jqm.png)
(where a and b are the sides and C is the included angle)
Given:
- a = 8
- b = 8
- C = ∠ABC = 120°
Substituting values into the formula:
![\implies \frac12\cdot 8 \cdot 8 \sin(120)=16√(3) \ \sf cm^2](https://img.qammunity.org/2023/formulas/mathematics/high-school/grv9v8iy52lp4h0zxmwuku0fvnnzw21omf.png)