Question

An exterior angle of a triangle is ${115}^{\circ }$ and one of the opposite angles is ${35}^{\circ }$. Find the other two angles.
(3 marks)

Answer 1

(0.5 mark)

$\angle ACE={115}^{\circ }and\angle A={35}^{\circ }$

$\angle ACE=\angle A+\angle B$
(Exterior angle is equal to sum of interior opposite angles) (1 Marks)

$\Rightarrow {115}^{\circ }={35}^{\circ }+\angle B$

$\Rightarrow \angle B={80}^{\circ }$ (0.5 mark)

In $\Delta ABC$,

$\angle A+\angle B+\angle C={180}^{\circ }$ (Angle sum property)

$\Rightarrow {35}^{\circ }+{80}^{\circ }+\angle C={180}^{\circ }$

$\Rightarrow {115}^{\circ }+\angle C={180}^{\circ }$

$\Rightarrow \angle C={65}^{\circ }$
(1 Marks)

Hence, the other two angles are ${80}^{\circ }$​ and ${65}^{\circ }$​.