Question

the measure of the angles of a triangle are in the ratio 1:2:3. prove thatit is a right angle triangle.​

Answer 1

Step-by-step explanation:

Let the three angles of the triangle be x,2x,3x

Therefore,

x+2+3x=180°[Angle sum property of triangle]

=>6x=180°

=>x=30°

Hence the three angles are x=30°,2x=60°,3x=90°

Hence, The given triangle is an right angled triangle.

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Answer 2

Answer :

• The angles are 30⁰ , 60⁰ , 90⁰
• The triangle is a right angled triangle

Given :

• The measure of the angles of a triangle are in the ratio 1 : 2 : 3

To prove :

• Triangle is right angled

Solution :

Given

The measure of the angles of a triangle are in the ratio 1 : 2 : 3 so,

• Let the angles of a triangle be x , 2x and 3x

We know that

• Sum of all angles in a triangle is equal to 180⁰

According to question

➞ x + 2x + 3x = 180⁰

➞ 6x = 180⁰

➞ x = 180⁰/6

➞ x = 30⁰

• x = 30⁰
• 2x = 2(30⁰) = 60⁰
• 3x = 3(30⁰) = 90⁰

The angles are 30⁰ , 60⁰ , 90⁰

Hence,The triangle is a right angled triangle

Verification :

➞ x + 2x + 3x = 180⁰

➞ 30⁰ + 2(30⁰) + 3(30⁰) = 180⁰

➞ 30⁰ + 60⁰ + 90⁰ = 180⁰

➞ 180⁰ = 180⁰

Hence,Verified