Question

If the sides of $△KLM$ are produced to $P,Q$ and $R$ as shown, find the sum of exterior angles $\angle 1,\angle 2$ and $\angle 3$.

Answer 1

Here, $\angle 1=\angle KLM+\angle KML$

$\angle 2=\angle LKM+\angle LMK$

$\angle 3=\angle MKL+\angle MLK$

Therefore,

$\angle 1+\angle 2+\angle 3=2(\angle LKM+\angle KML+\angle MLK)$

$\angle 1+\angle 2+\angle 3=2\times {180}^o={360}^o$