Question

The angles of a triangle are in ratio 3:2:1. Find all the angles of a triangle. what type
of triangle it is?

Answer 1

Answer:

The smallest angle is

∠

C

=

30

°

Explanation:

Let the triangle be

Δ

A

B

C

and angles be

∠

A

,

∠

B

,

∠

C

Now, we know that all the 3 angles of a triangle sum up to be

180

°

from the Triangle Sum Property.

∴

∠

A

+

∠

B

+

∠

C

=

180

∴

3

x

+

2

x

+

x

=

180

... [Given that the ratio of angles is

3

:

2

:

1

]

∴

6

x

=

180

∴

x

=

180

6

∴

x

=

30

°

Now assigning the angles their values,

∠

A

=

3

x

=

3

(

30

)

=

90

°

∠

B

=

2

x

=

2

(

30

)

=

60

°

∠

C

=

x

=

(

30

)

=

30

°

Now, as we can clearly observe, the smallest angle is

∠

C

which is

=

30

°

Hence, the smallest angle is of

30

°

.

Answer 2

Answer:

Let the angles of the triangle be 3x, 2x and x

We know that the sum of the angles of the triangle is 180°.

According to the problem,

3x+2x+x=180

6x=180

x=30

Therefore, the angles are 90°, 60° and 30°.

The triangle is a right-angle triangle.