Question

2.
opposite angles
the angles of the triangle.
The three angles of a triangle are in the ratio 2:1:2. Find the measure of the angles and state the kind of triangle
3.
ndithe following can be the measure of the sofa triangle Give reasons.​

Answer 1

Correct Question:

The three angles of a triangle are in the ratio 2:1:2. Find the measure of each angle and state what type of triangle it is.

Answer:

Angle measures = 72°, 36°, 72°

Type of triangle = Acute angled triangle

Solution:

Let the three angles of the triangle be 2x, 1x and 2x. ------ (1)

We know that the sum of all the angles of a triangle is 180°. ------ (2)

Combining statements (1) and (2):

2x + 1x + 2x = 180°

5x = 180°

x = 180/5

x = 36

So,

2x = 2 x 36 = 72°

1x = 1 x 36 = 36°

2x = 2 x 36 = 72°

Hence the three angles of the triangle are 72°, 36° and 72°.

As all the angles are below 90°, it is an acute angled triangle.

Knowledge Bytes:

→ Classification of triangles on basis of angles:

✳ Acute angled triangle

A triangle that has all the measures below 90° is known as an acute angled triangle.

✳ Right angled triangle

A triangle that has one angle equal to 90° is known as a right angled triangle.

✳ Obtuse angled triangle

A triangle that has one angle more than 90° is known as obtuse angled triangle.

→ Angle Sum Property of Triangles

The sum of all the angles of a triangle is 180°.