Question

6.
The angles of a triangle are in the ratio 3:7: 8. Find the greatest and the smallest angles.
The sum of the angles of a triangle is 180°.
​

Answer 1

Given:

The angles of a triangle are in the ratio 3:7:8

To Find:

Greatest Angle=?

Smallest Angle=?

Solution:

Let the angles be x.

Therefore,

3x+7x+8x=180°.....(Sum of all angles of a triangle is 180°)

18x=180°

x=180°/18

x=10°

So the ,

Smallest Angle=3x=3×10=30°

Greatest Angle=8x=8×10=80°

Answer 2

Given: Ratio of angles of triangle= 3:7:8

To find: Greatest and smallest angle=?

Solution: Let us consider the angles of the triangle be 3x, 7x and 8x respectively according to ratio.

Now we know that,

The sum of the angles of a triangle is 180°.

So, according to the above property,

3x + 7x +8x = 180°

18x =180°

x = 180 /18

x= 10

Greatest angle= 8x

= 8× 10

= 80°

Smallest angle = 3x

= 3× 10

= 30°

Thus, the greatest angle is 80° and the smallest angle is 30° respectively.

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