Let's write the relation between the exterior angle ∠PRS and the interior opposite angles –

Given ΔPRS

To find the relation between the exterior angle ∠PRS and the interior opposite angles

We know in a triangle the sum of all three interior angles is equal to 180°.

So in ΔPRS,

∠PQR+∠QRP+∠RPQ=180°

⇒ ∠PQR+∠RPQ =180°-∠QRP………….(i)

Now QRS is a straight line, so

∠QRS=180°

⇒ ∠QRS=∠QRP+∠PRS=180°

⇒ ∠PRS=180°-∠QRP………(ii)

Substituting equation (ii) in equation (i), we get

∠PQR+∠RPQ=∠PRS

Hence the measure of any exterior angle of a triangle is equal to the sum of the measures of its two interior opposite angles.