Lines and Angles • Topic 3 of 3

Angle Sum Property of a Triangle

What is the Angle Sum Property?

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

Mathematically: ∠A + ∠B + ∠C = 180°

Why is this true?

  • Draw a line through one vertex parallel to the opposite side
  • Alternate interior angles formed with this parallel line are equal to the triangle's angles
  • These three angles together form a straight line (180°)

Exterior Angle Theorem:

An exterior angle of a triangle is formed by extending one side. The exterior angle equals the sum of the two opposite interior angles (called remote interior angles).

Exterior Angle Theorem: ∠ACD = ∠A + ∠B

Real-Life Applications:

  • Navigation and triangulation
  • Architecture (roof trusses, bridges)
  • Surveying and map-making
Angle Sum Property of a TriangleABC∠A∠B∠Cl ∥ BCProof: Draw line l through A, parallel to BC∠DAB = ∠ABC (alternate interior angles, l ∥ BC)∠EAC = ∠ACB (alternate interior angles)∠DAB + ∠BAC + ∠EAC = 180° ∴ ∠A + ∠B + ∠C = 180°
Solved Examples
1
Worked Example

Solve a standard problem on Angle Sum Property of a Triangle.

Solution

Apply the formula/method shown in the concept section above.

Key Points

  • Understand the definition and properties of Angle Sum Property of a Triangle.
  • Study the worked examples and practice similar problems.
  • Always verify your answer using the original conditions.
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The sum of the angles of a triangle is:
Explanation: Always $180^\circ$.
Q2.An exterior angle equals the sum of the two:
Explanation: Exterior-angle theorem.
Q3.If two angles of a triangle are $50^\circ$ and $60^\circ$, the third is:
Explanation: $180-110=70$.
Q4.Each angle of an equilateral triangle is:
Explanation: $60^\circ$.
Practice more MCQs → 📝 Assignment · 35 marks