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 ways

Answer 1

$\mathbb{ SOLUTION }$ :

$\bf{Given }$ :
Three angles of a triangle are in ratio 1:2:1

Let,
first angle be 1x°
second angle be 2x°
third angle be 1x°

$\bf{We \:know\: that, }$
Sum of all the angles of a triangle is 180°

So,
=> 1x + 2x + 1x = 180°

=> 4x = 180°

=> x = 180 ÷ 4

=> x = 45°

$\therefore$ first angle = 1x° = 1*45 = 45°
$\therefore$ second angle = 2x° = 2*45 = 90°
$\therefore$ third angle = 1x° = 1*45 = 45°

Now,
one angle of the triangle is 90° so it is an right angled triangle.

and

two angles are equal, so it is also a isosceles triangle.

$\therefore$ The triangle is a isosceles right triangle

Answer 2

Here is your solution

Given :-

Three angles of a triangle are in ratio 1:2:1

Let, 

First angle = x°

Second angle = 2x°

Third angle be =x°

We know that

The Sum of all the angles of a triangle is 180°

A/q

=> 1x + 2x + 1x = 180°

=> 4x = 180°

=> x = 180/4

=> x = 45°

First angle=> x° = 45 = 45°

Second angle=>2x°=2×45=90°

Third angle => x° = 45°

Our observation is :-

One angle of the triangle is 90° and two angles are equal.

it is an right angled triangle. & isosceles triangle

Hence

it is right isosceles triangle

Hope it helps you