Question

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 way

Answer 1

your answer is
let the angle in ratio be 'x'
so,x+2x+x=180°
4x=180°
x=45°

so,2x=90°

the triangle is isosceles
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Answer 2

Ratio of the angles 1 : 2 : 1 (given)

Define x:

Ratio of the angles 1 : 2 : 1

Let x be the constant ratio

Ratio of the angles 1x : 2x : 1x

Solve x:

Sum of angles in a triangle = 180º

1x + 2x + 1x = 180

4x = 180

x = 45º

Find the angles:

1x = 45º

2x = 2(45) = 90º

1x = 45º

⇒  The angles are 45º, 90º and 45º

Classify the triangle:

1) Since there are 2 angles that are equal

   ⇒ It is an isosceles triangle

2) Since there is one right angle

  ⇒ It is a right angle triangle

Answer: The angles are 45º, 90º and 45º. It is an isosceles triangle and it is also a right angle triangle.