Question

The smallest angle of a triangle is 30 degrees. The angles of the triangle are in A.P. The triangle is A. isosceles B. right angled C. equilateral D. Scalene

Answer 1

Answer:

It is a (D)Scalene Triangle.

And, its angles are:- 90°, 60° and 30°.

Step-by-step explanation:

Suppose the angles are:- x, (x+h) and (x-h)

And, smallest angle = x-h = 30° ..........(1)

Thus,

x + (x+h) +(x-h) = 180°

x + (x+h) + 30 = 180°

2x + h = 150° ............(2)

Add (1) and (2),

3x = 180

=> $\fbox{x = 60°}$

Put x = 60° in (1),

60 - h = 30

$\fbox{h = 30}$

Thus,

Angles of Triangle = x, (x+h), (x-h)

= 60°, (60+30)°, (60-30)°

$\fbox{Angles = 60°, 90°, 30°}$

Thus, after investigating the Angles of the triangle, it is clear that it is a Scalene Triangle.

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