Question

If one angle of a triangle is equal to the sum of the other two, show that the triangle is right-angled.



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Answer 1

Answer: Consider ABC as a triangle

According to the question, it can be written as

∠A=∠B+∠C....(1)

We know that the sum of all the angles in a triangle is 180  

 

So we can write it as

∠A+∠B+∠C=180  

 

By substituting ∠A in the above equation

∠B+∠C+∠B+∠C=180  

 

2(∠B+∠C)=180  

 

By division

∠B+∠C= 180/2  

 

∠B+∠C=90

   

According to equation (1), we can write it as  

∠A=90

   

Therefore, it is proved that the triangle is right-angled.

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