Question

Angles of a triangle are in the ratio 4 : 6 : 5 . the triangle is :
A. an acute angle triangle
B. an obtuse angle triangle
C. right angle triangle
D. isosceles triangle

Answer 1

Hint: The sum of interior angle of the triangle is 180 degree.
>Acute angled triangle = those triangles whose all angles are less then 90 degree
>right angled triangle = those triangles whose one angle is 90 degree
>obtuse angled triangle = those triangles whose one angle is more the 90 degree
>isosceles angled triangle = those triangles whose two side are equal

Complete answer: Since the ratios of the angles of the triangle are 4 : 6 : 5
So let the angles of the triangle be 4x , 6x , 5x
And we know that the sum of interior angle of the triangle is 180 degree
Then ,
4x + 6x + 5x = 180
15x = 180

X = 12 degree
So the angles of the triangle are
4x = 4 * 12 = 48 degree
6x = 6 * 12 = 72 degree
5x = 5 * 15 = 60 degree
Since we can see that all the angles are less than 90 degree
So the triangle is acute angled triangle

Hence, option (A) is correct

Note: We have to keep in mind that the sum of interior angles of a triangle is 180 degree.
Also keep in mind that acute triangle is that triangle in which all angles of a triangle are less than 90 degree and the obtuse triangle is that triangle in which one angle of the triangle is greater than 90 degree.