Exterior angle property

key notes :

🌟 Exterior Angle Property

🧮 What is an Exterior Angle?

• An exterior angle of a triangle is the angle formed outside the triangle when one side of the triangle is extended.
  👉 Example: If side BC of triangle ABC is extended to point D, then ∠ACD is an exterior angle.

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📏 Exterior Angle Property

👉 The measure of an exterior angle of a triangle is equal to the sum of the two opposite interior angles.

✨ Formula:

Exterior Angle = Sum of two opposite Interior Angles

🟩 Example:

If in triangle ABC, side BC is extended to D,
then

∠ACD = ∠A + ∠B

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💡 Important Notes

• The exterior angle and its adjacent interior angle form a linear pair (sum = 180°).
• There can be three exterior angles in a triangle, one at each vertex.
• The sum of all exterior angles of a triangle (one per vertex) is 360°.

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🔢 Example Problem

In △ABC, side BC is extended to D.
If ∠A = 50° and ∠B = 60°,
then

∠ACD = ∠A + ∠B = 50° + 60° = 110°

✅ Answer: 110°

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🧠 Real-life Connection

🛣️ The concept of exterior angles helps in:

• Architecture 🏗️ (designing triangular roof structures)
• Navigation 🧭 (finding direction turns)
• Engineering ⚙️ (calculating forces and support angles)

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🏁 Summary

🟢 Concept	🧠 Description
Exterior Angle	Formed by extending one side of a triangle
Property	Exterior angle = sum of two opposite interior angles
Linear Pair	Exterior + Adjacent Interior = 180°
Sum of all Exterior Angles	360°

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✨ Remember:

“The outside (exterior) angle always equals the sum of the two far-away (interior) angles!” 💫

Learn with an example

Let’s practice!