Angles in Parallel Lines & Triangles • Topic 2 of 2

Triangle Angle Sum & Exterior Angle Theorem

Triangle Angle Sum Theorem: The three interior angles of any triangle always add up to 180 degrees.

Angle A + Angle B + Angle C = 180 degrees

Exterior Angle Theorem: An exterior angle of a triangle equals the sum of the two non-adjacent (remote) interior angles.

This is because the exterior angle and its adjacent interior angle form a straight line (180 deg), and that interior angle plus the other two = 180 deg.

TRIANGLE ANGLE SUM:

        C
        /\
       /  \
      / 60  \
     /        \
    A____50____B
          70

  50 + 60 + 70 = 180 degrees

EXTERIOR ANGLE THEOREM:

    C
    /\
   /  \
  A----B----D
           ^
   Exterior angle at D = angle A + angle C
Solved Examples
1
Worked Example
Triangle has angles 45 and 75 degrees. Find the third angle.
SolutionThird angle = 180 - 45 - 75 = 60 degrees.
2
Worked Example
In a triangle, one angle is twice another, and the third angle is 30 degrees. Find all angles.
SolutionLet angles be x, 2x, 30. x + 2x + 30 = 180 => 3x = 150 => x = 50. Angles: 50, 100, 30 degrees.
3
Worked Example
An exterior angle of a triangle is 130 degrees, and one remote interior angle is 55 degrees. Find the other remote interior angle.
Solution130 = 55 + other angle => other angle = 75 degrees.

Key Points

  • Sum of interior angles in any triangle = 180 degrees
  • Exterior angle = sum of the two non-adjacent interior angles
  • Can use algebra to find missing angles
  • The largest angle is always opposite the longest side
Quick Check — 4 MCQs
Tap an option to check your answer0 / 4
Q1.The angle sum of a triangle is:
Explanation: $180^\circ$.
Q2.An exterior angle equals the sum of the two:
Explanation: Opposite interior angles.
Q3.If two angles are $50^\circ$ and $60^\circ$, the third is:
Explanation: $180-110=70$.
Q4.The three exterior angles of a triangle sum to:
Explanation: $360^\circ$.
Practice more MCQs → 📝 Assignment · 35 marks