Triangle angle-sum property

key notes :

1️⃣ Definition:

👉 The angle-sum property of a triangle states that the sum of the three interior angles of a triangle is always 180°. 🎯

∠A + ∠B + ∠C = 180°

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2️⃣ 💡 Important Concept:

• This rule applies to all types of triangles — 🔹 acute, 🔸 right, and 🔺 obtuse triangles.
• Even if the sides or angles change, the total sum of interior angles remains constant (180°)! 🔥

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3️⃣ 📐 Examples:

• Example 1: If ∠A = 60°, ∠B = 70°, find ∠C.
  ✏️ ∠C = 180° – (60° + 70°) = 50° ✅
• Example 2: If ∠A = 90°, ∠B = 45°, find ∠C.
  ✏️ ∠C = 180° – (90° + 45°) = 45° ✅

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4️⃣ 🌟 For Exterior Angles:

👉 The exterior angle of a triangle equals the sum of the two opposite interior angles.

Exterior angle = ∠1 + ∠2

🧠 Example: If one exterior angle = 120°, and one interior opposite angle = 50°,
then the other opposite angle = 120° – 50° = 70° ✨

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5️⃣ 🧩 Real-Life Connection:

Triangles are everywhere! 🏠

• Roofs, signboards, and bridges use triangular shapes because they’re strong and stable — and this property helps engineers calculate angles perfectly! 💪📏

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6️⃣ 🎯 Key Takeaways:

✅ The sum of interior angles of a triangle = 180°
✅ The exterior angle = sum of two opposite interior angles
✅ Applies to all types of triangles
✅ Used in geometry, design, and construction

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💬 Mnemonic to Remember:

🌀 “All Triangles Add Up to 180!” 🌀

Learn with an example

Let’s practice!