Question

What are the angles of an isosceles right angled triangles?

Answer 1

Given: ΔPQR is an isosceles right-angled triangle.

We know that in an isosceles triangle, two sides are of equal length.

In ΔPQR, PQ = QR

Also, angles opposite to equal sides of an isosceles triangle are equal.

⇒∠QRP = ∠QPR

Using angle sum property in ΔPQR, we have:

∠PQR + ∠QRP + ∠RPQ = 180°

⇒ 90° + 2∠QRP = 180°

⇒ 2∠QRP = 180° − 90°

⇒ ∠ QRP = = 45°

Thus, the angles of an isosceles right-angled triangle are 45°, 90° and 45°.