UPSC CDS 2 2020 Math Paper

Concept:
Sum of interior angle of triangle =180∘
Calculation:
1) 1:2:3
So, x+2x+3x=6x
Then 6x=180∘,x=30∘
Angles 30∘,60∘ and 90∘
2) 3:4:5
So, 3x+4x+5x=180∘
Then 12x=180∘,x=15
Angles 45∘,60∘ and 75∘
3) 5:6:7
So, 5x+6x+7x=180∘
Then 18x=180∘,x=10∘
Angles 50∘,60∘ and 70∘
4) 6:7:8
So, 6x+7x+8x=180∘
Then 21x=180∘,x=8.57∘
Angles 51.42∘,59.99∘ and 68.57∘
∴ Option 4 is not integer angle in triangle.