Question

Derive the angle sum property of the triangle using the exterior angle property of the triangle. [4 MARKS]

Answer 1

Visualizing the question into diagram : 1 Mark
Properties : 1 Mark
Steps : 1 Marks
Proof : 1 Marks



$\angle 1$, $\angle 2$ and $\angle 3$ are angles of triangle ABC and 4 is the exterior angle when BC is extended to D.
$\angle 1$ + $\angle 2$ = $\angle 4$ (Exterior Angle Property)
$\angle 1$ + $\angle 2$ + $\angle 3$ = $\angle 4$ + $\angle 3$ (Adding $\angle 3$ to both sides)
Also, $\angle 3$ + $\angle 4$ = 180${}^o$ (Linear Pair of angles)
$\therefore$ $\angle 1$ + $\angle 2$ + $\angle 3$ = 180${}^o$