Question

Prove that in any triangle, cash external angle is equal to the sum of the internal angles at the other two vertices.

Answer 1

Consider ΔPQR:

In ΔPQR, by angle sum property, we have:

∠QPR + ∠PQR +∠QRP = 180°

⇒ ∠QRP = 180° − ∠PQR − ∠QPR ... (1)

Also, ∠PRT and ∠PRQ are forming a linear pair.

⇒ ∠PRT + ∠PRQ = 180°

⇒∠PRT + 180° − ∠PQR − ∠QPR = 180° (Using equation (1))

⇒∠PRT = ∠PQR + ∠QPR

Hence, in any triangle, each external angle is equal to the sum of the internal angles at the other two vertices.