Correct Answer – Option 1 : Acute angle triangle

Given:

The angle of the triangle are in the ratio = 4 ∶ 5 ∶ 6

Concept used:

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

An acute–angled triangle is a type of triangle in which all the three internal angles of the triangle are acute, i.e less than 90°

An obtuse-angled triangle is a triangle in which one of the interior angles measures more than 90° 

A right triangle or right-angled triangle is a triangle in which one angle is a right angle

An isosceles triangle is a triangle that has two sides of equal length

Calculations:

The sum of angles of triangle = 180°

The sum of the angles = (4x + 5x + 6x) 

⇒ 15x 

15x = 180° 

⇒ x = 180°/15

⇒ x = 12

Hence angles in the triangle are 4x, 5x, 6x = 48, 60, and 72 

In a triangle, If all the three angles are less than 90° then, the triangle is known as Acute angle triangle

∴ The triangle is an Acute triangle.