Exterior Angles of Triangles
Grade 4What is an exterior angle?
An exterior angle of a triangle is formed by extending one side of the triangle beyond the vertex. It sits outside the triangle, adjacent to an interior angle.
The key rule: the exterior angle of a triangle equals the sum of the two non-adjacent interior angles. This is sometimes called the exterior angle theorem.
Why does it work?
The three interior angles sum to 180°. The exterior angle and its adjacent interior angle also sum to 180° (angles on a straight line). So the exterior angle must equal what is left over — the other two interior angles.
Worked example
Try this one
The diagram shows a straight line XY and two lines PA and QB that are parallel to each other. A transversal meets PA at point G and QB at point H. Angle PGH = \( (9k - 5)^\circ \) and angle GHB = \( (6k + 25)^\circ \).
Angle PGH and angle GHB are alternate angles.
Find the value of \( k \) and the size of angle GHB. [4]
The question tells you these are alternate angles between parallel lines.
Ask yourself: 'What is always true about alternate angles — do they add to 180° or are they equal to each other?' Use that fact to set up an equation, then solve for k and substitute back.
