Question

find the measure of all angle of a triangle which are in the ratio 1:2:3.​

Answer 1

Answer:

30 60 90

Step-by-step explanation:

Let the angles of the triangle be x , 2x and 3x .

We know that from angle sum property of of a triangle

sum of all three angles of a triangle is 180

x + 2x + 3x = 180

6x = 180

x = 30

2x = 60 .

3x = 90

So the angles of a triangle are 30° , 60° and 90°

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Answer 2

Answer-

Concept used- Angle Sum of Property of a Triangle

Triangle- It is a three-sided polygon.

Characteristics of a triangle:

1. It has three sides.

2. It has three angles.

3. It has three vertices.

Let us consider a triangle ABC whose angles are ∠A, ∠B and ∠C.

Given ratio: 1:2:3

⇒ Let ∠A= x, ∠B= 2x and ∠C= 3x

We know that angle sum property of a Δ is 180°.

So, in ΔABC,

∠A + ∠B + ∠C = 180°

x + 2x + 3x = 180°

6x= 180°

x= 180° ÷ 6 = 30°

Putting value of x, we get,

∠A= 30°

∠B= 60°

∠C= 90°

(This also tells that Δ is right-angled at C.)

∴ Three angles of Δ are 30°, 60° and 90°.