The three angles of a triangle are in the ratio 1:2:1. Find all the an

1.	The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle. Classify the triangle in two different ways.
Answer» Let the angles of the triangle be x, 2x, x. Using the angle sum property, we have x + 2x + x = 180° 4x = 180° x = \(\frac{180°}{4}\) x = 45° 2x = 2 x 45° = 90° Thus the three angles of the triangle are 45°, 90°, 45°. Its two angles are equal. It is an isoscales triangle. Its one angle is 90°. ∴ It is a right angled triangle.

The three angles of a triangle are in the ratio 1:2:1. Find all the angles of the triangle. Classify the triangle in two different ways.

Answer»

Let the angles of the triangle be x, 2x, x.

Using the angle sum property, we have

x + 2x + x = 180°

4x = 180°

x = \(\frac{180°}{4}\)

x = 45°

2x = 2 x 45°

= 90°

Thus the three angles of the triangle are 45°, 90°, 45°.

Its two angles are equal. It is an isoscales triangle.

Its one angle is 90°.

∴ It is a right angled triangle.