Question

(a) Derive the angle sum property of the triangle using the exterior angle property.

(b) AE is the angular bisector. $\angle 4={140}^{\circ },\angle 2={60}^{\circ },\angle EAC=x$. Find $x$.


[4 MARKS]

Answer 1

(a) Steps: 1 Mark
Proof: 1 Mark
(b) Steps: 1 Mark
Result: 1 Mark


(a)


$\angle 1$, $\angle 2$ 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${}^o$


(b)

$\angle 1$ + $\angle 2$ = $\angle 4$ (Exterior Angle Property)
$\angle 1+{60}^{\circ }={140}^{\circ }$
$\angle 1={140}^{\circ }-{60}^{\circ }={80}^{\circ }$
Since AE is the angular bisector therefore $\angle EAC=\frac{\angle 1}{2}$
$\Rightarrow x=\frac{80}{2}={40}^{\circ }$