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Exterior Angle of a Triangle and Its Property

If the sides ...

Question

If the sides of $△ K L M$ are produced to $P, Q$ and $R$ as shown, find the sum of exterior angles $∠ 1, ∠ 2$ and $∠ 3$ .

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Solution

Here, $∠ 1 = ∠ K L M + ∠ K M L$
$∠ 2 = ∠ L K M + ∠ L M K$
$∠ 3 = ∠ M K L + ∠ M L K$
Therefore,
$∠ 1 + ∠ 2 + ∠ 3 = 2 (∠ L K M + ∠ K M L + ∠ M L K)$
$∠ 1 + ∠ 2 + ∠ 3 = 2 \times 180^{o} = 360^{o}$

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