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°
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°)! 🔥
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° ✅
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° ✨
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! 💪📏
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
💬 Mnemonic to Remember:
🌀 “All Triangles Add Up to 180!” 🌀
Learn with an example
The diagram shows a triangle.

What is the value of c?
c =_____°
First, look at the interior angle measures in the triangle.

Set the sum of the interior angle measures of the triangle equal to 180°. Solve for c.
c+84°+58° = 180°
c+142° = 180° Combine like terms
c = 38° Subtract 142° from both sides
So, c=38°.
The diagram shows a triangle.

What is the value of b?
b = ____°
First, look at the interior angle measures in the triangle.

Set the sum of the interior angle measures of the triangle equal to 180°. Solve for b.
67°+32°+b = 180°
b+99° = 180° Combine like terms
b = 81° Subtract 99° from both sides
So, b=81°.
The diagram shows a triangle.

What is the value of b?
b = ____°
First, look at the interior angle measures in the triangle.

Set the sum of the interior angle measures of the triangle equal to 180°. Solve for b.
b+98°+40° = 180°
b+138° = 180° Combine like terms
b= 42° Subtract 138° from both sides
So, b=42°.

Let’s practice!