Question

Prove that the exterior angle of a triangle is equal to the sum of two interior opposite angles.

Accepted Answer

Consider a $∆ PQR$ , in which $∠ P, ∠ Q, ∠ R$ are the interior angles and $∠ PRS$ is the exterior angle.

We need to prove, $∠ PRS = ∠ P + ∠ Q$ .

Now, let us mark the angles as follows:

$∠ P = ∠ 1, ∠ Q = ∠ 2, ∠ R = ∠ 3$ and $∠ PRS = ∠ 4$

According to the interior angle property of a triangle, the sum of the interior angles of a triangle is $180 °$ .

$\Rightarrow ∠ 1 + ∠ 2 + ∠ 3 = 180 ° . . . . . . . . . . (i)$

We know that sum of the angles in a linear pair is equal to $180 °$ .

$\Rightarrow ∠ 3 + ∠ 4 = 180 ° . . . . . . . . . . . . (i i)$

Then, from equations $(i)$ and $(i i)$ , we get,

$∠ 1 + ∠ 2 + ∠ 3 = ∠ 3 + ∠ 4$

$\Rightarrow ∠ 1 + ∠ 2 = ∠ 4 (∵ ∠ 3$ from both sides gets eliminated $)$

$∴ ∠ P + ∠ Q = ∠ PRS$ .

Hence, proved.

Chhattisgarh Board Solutions for Exercise 5: Try These

Chhattisgarh Board Mathematics Solutions for Exercise - Chhattisgarh Board Solutions for Exercise 5: Try These

Questions from Chhattisgarh Board Solutions for Exercise 5: Try These with Hints & Solutions

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