Question

The angles of some triangles are given below. Classify each of the triangles as acute angled, obtuse angled or right angled on the basis of its angles.
i) \[{90^ \circ },{45^\circ },{45^\circ }\]_________________________
ii) \[{80^\circ },{60^\circ },{40^\circ }\]_________________________
iii) \[{120^\circ },{50^\circ },{10^\circ }\]_________________________
iv) \[{60^\circ },{60^\circ },{60^\circ }\]__________________________
v) \[{92^\circ },{50^\circ },{38^\circ }\]___________________________
vi) \[{90^ \circ },{35^\circ },{55^\circ }\]____________________________

Answer 1

Hint: Here we will observe the angles of each of the triangles.
If one of the angles is \[{90^\circ }\]then it is a right angled triangle.
If all the angles are less than \[{90^\circ }\]\[\left( { < {{90}^\circ }} \right)\]then it is an acute angled triangle.
If any one of the angles is greater than \[{90^\circ }\]\[\left( { > {{90}^\circ }} \right)\]then it is an obtuse angled triangle.

Complete step by step solution:
i) The given angles are: \[{90^ \circ },{45^\circ },{45^\circ }\]
Here since one of the angles is \[{90^\circ }\] therefore it is a right angled triangle.

ii) The given angles are: \[{80^\circ },{60^\circ },{40^\circ }\]
Here, all the angles are less than \[{90^\circ }\]\[\left( { < {{90}^\circ }} \right)\]then it is an acute angled triangle.

iii) The given angles are: \[{120^\circ },{50^\circ },{10^\circ }\]
Here, one of the angles is greater than \[{90^\circ }\]\[\left( { > {{90}^\circ }} \right)\]then it is an obtuse angled triangle.

iv) The given angles are: \[{60^\circ },{60^\circ },{60^\circ }\]
Here, all the angles are less than \[{90^\circ }\]\[\left( { < {{90}^\circ }} \right)\] then it is an acute angled triangle.
Also, since all the angles are equal therefore it is an equilateral triangle.

v) The given angles are: \[{92^\circ },{50^\circ },{38^\circ }\]
Here, one of the angles is greater than \[{90^\circ }\] \[\left( { > {{90}^\circ }} \right)\] then it is an obtuse angled triangle.

vi) The given angles are: \[{90^\circ },{35^\circ },{55^\circ }\]
Here since one of the angles is \[{90^\circ }\] therefore it is a right angled triangle.

Note:
In a triangle, if all the angles are equal or each angle of the triangle is \[{60^\circ }\] then it is an equilateral triangle.
In a triangle, if any two of the angles are equal then it is an isosceles triangle.
In a triangle, if any one of the angles is \[{90^\circ }\]then it is a right angled triangle.
In a triangle, if none of the angles are equal then it is a scalene triangle.