Question

In a triangle, if an angle is the average of the other two angles and the difference between the greatest and the least angle is
60
∘
, then it is:

An isosceles triangle
An equilateral triangle
A right-angled triangle
A right-angled isosceles triangle

Answer 1

Answer:

Let least angle of the triangle be x

∘

Greatest angle = x

∘

+60

∘

Third angle =

2

x

∘

+x

∘

+60

∘

=x

∘

+30

∘

We have,

x

∘

+x

∘

+30

∘

+x

∘

+60

∘

=180

∘

3x

∘

+90

∘

=180

∘

x=30

∘

The angles are 30

∘

,60

∘

,90

∘

∴ one of the angle is 90

∘

, so the triangle formed is a right angled triangle.

Answer 2

Given; In a triangle, if an angle is the average of the other two angles and the difference between the greatest and the least angle is

60

To Find; Which type of triangle is this

Solution; let one angle=x

Then the greatest angle=60+x

Third angle=30+x

Angels sum of triangle =180°

x+60+x+30+x=180°

3x=90°

x=30°

So the angels are 30 90 and 60 here one angle is right-angled

Hence the given triangle is right-angled