Question

The angles of some triangles are given below. Classify each triangle acute-angled,obtuse-angled or right-angled on the basis of its angles.
$\begin{array}{c}a.{90}^{\circ },{45}^{\circ },{45}^{\circ }\\ b.{60}^{\circ },{60}^{\circ },{60}^{\circ }\\ c.{80}^{\circ },{60}^{\circ },{40}^{\circ }\\ d.{92}^{\circ },{50}^{\circ },{38}^{\circ }\\ e.{120}^{\circ },{50}^{\circ },{10}^{\circ }\\ f.{90}^{\circ },{35}^{\circ },{55}^{\circ }\end{array}$

Answer 1

A triangle with angles less than ${90}^{\circ }$ are called acute-angled triangle.

A triangle with ${90}^{\circ }$ angle is called right-angled triangle.

A triangle with angle greater than ${90}^{\circ }$ are obtuse-angled triangle.

A triangle with all equal angles is called equilateral triangle.

Using the above definitions to classify the triangles in the question:

a) ${90}^{\circ },{45}^{\circ },{45}^{\circ }$-Right angled triangle.

b) ${60}^{\circ },{60}^{\circ },{60}^{\circ }$ - equilateral triangle (acute angle)

c) ${80}^{\circ },{60}^{\circ },{40}^{\circ }$ - acute angled triangle (all angles $<{90}^{\circ }$)

d) ${92}^{\circ },{50}^{\circ },{38}^{\circ }$ - obtuse angled triangle (one angle $>{90}^{\circ }$)

e) ${120}^{\circ },{50}^{\circ },{10}^{\circ }$ - obtuse angled triangle (one angle $>{90}^{\circ }$)

f) ${90}^{\circ },{35}^{\circ },{55}^{\circ }$ - right angled triangle (angle $={90}^{\circ }$)