Question

In a triangle, values of all the angles are integers (in degree measure). Which one of the following cannot be the proportion of their measures?
1. 1 ∶ 2 ∶ 3
2. 3 ∶ 4 ∶ 5
3. 5 ∶ 6 ∶ 7
4. 6 ∶ 7 ∶ 8

Answer 1

Correct Answer - Option 4 : 6 ∶ 7 ∶ 8

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 integar angle in triangle.