Calculate interior and exterior angles in polygons.

Let’s solve each part step by step.

We are dealing with polygons and their interior/exterior angles.

Key facts:
- The sum of exterior angles of any polygon is always 360°.
- For a regular polygon (all sides and angles equal), each exterior angle = 360° ÷ number of sides.
- Interior angle + exterior angle = 180° (they form a straight line).
- So, if we know the exterior angle, interior = 180° – exterior.
- If we know the interior angle, exterior = 180° – interior.

Also, for a regular polygon with n sides:
→ Interior angle = (n – 2) × 180° ÷ n

But since all figures here look regular, we’ll assume they are regular polygons unless told otherwise.

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Part a): Pentagon (5 sides), angle ‘a’ is an exterior angle.

Exterior angle of regular pentagon = 360° ÷ 5 = 72°
So, a = 72°

Wait — let’s check: Is ‘a’ really the exterior angle? Looking at the diagram description: it’s marked outside the polygon, between one side and the extension of the adjacent side → yes, that’s an exterior angle.

✔ a = 72°

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Part b): Hexagon (6 sides), angle ‘b’ is an exterior angle.

Exterior angle = 360° ÷ 6 = 60°
So, b = 60°

✔ b = 60°

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Part c): Hexagon again (6 sides), angle ‘c’ is an interior angle.

Interior angle of regular hexagon = (6 – 2) × 180° ÷ 6 = 4 × 180° ÷ 6 = 720° ÷ 6 = 120°
Alternatively: since exterior is 60°, interior = 180° – 60° = 120°

✔ c = 120°

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Part d): Decagon? Let’s count the sides.

Pink shape: looks like a decagon (10 sides). Let me confirm: from the image description, it’s a pink polygon with 10 sides — yes, decagon.

Angle ‘d’ is an interior angle.

Interior angle of regular decagon = (10 – 2) × 180° ÷ 10 = 8 × 180° ÷ 10 = 1440° ÷ 10 = 144°

Alternatively: exterior angle = 360° ÷ 10 = 36°, so interior = 180° – 36° = 144°

✔ d = 144°

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Final check:

a) Pentagon → exterior = 360/5 = 72° → correct
b) Hexagon → exterior = 360/6 = 60° → correct
c) Hexagon → interior = 180 - 60 = 120° → correct
d) Decagon → interior = 180 - 36 = 144° → correct

All calculations verified.

Final Answer:
a) 72°, b) 60°, c) 120°, d) 144°