Exterior angle — Grade 8 Math, what it means and where it is taught
The angle formed by extending one side of a triangle.
Taught in Grade 8 Math.
Where it is taught
Practise this idea
7 questions in the course bank use Exterior angle, in Geometric Construction, Angle Relationships, Quadrilaterals & Polygon Properties.
Problem 1
A triangle has interior angles of 60° and 70°. Find the exterior angle at the third vertex.
Worked answer
130
Third interior angle: 180 - 60 - 70 = 50°
Exterior angle: 180 - 50 = 130°
Or directly: 60 + 70 = 130° ✓
Problem 2
A triangle has interior angles 38° and 59°. Find the exterior angle at the third vertex.
Worked answer
97
38 + 59 = 97
97°
Problem 3
An exterior angle of a triangle is 128° and one remote interior angle is 55°. Find the other remote interior angle.
Worked answer
73
128 - 55 = 73
73°
Problem 4
Find the sum of the exterior angles of any convex polygon.
Worked answer
360
You turn through one full circle.
360°, whatever n is.
Problem 5
Find each exterior angle of a regular octagon.
Worked answer
45
360 ÷ 8 = 45°
Problem 6
Find each interior angle of a regular decagon.
Worked answer
144
Exterior: 360 ÷ 10 = 36
Interior: 180 - 36 = 144°
Problem 7
A regular polygon has each interior angle 156°. How many sides?
Worked answer
15
Exterior = 180 - 156 = 24
360 ÷ 24 = 15