Question

the angle of the ratio are 2:3:7find the measure of the smallest angle

Answer 1

30°

Step-by-step explanation:

Correct question :-

The angles of the triangle are in ratio 2 : 3 : 7, find the measure of the smallest angle.

Solution -

Let the three angles as 2x, 3x and 7x respectively

Sum of all angles of triangle = 180°

=> 2x + 3x + 7x = 180°

=> 12x = 180°

=> x = 180/12°

=> x = 15°

The smallest angle = 2x = 2×15° = 30°

Hence the measure of smallest angle is 30°.

hope it helps.

Answer 2

Step-by-step explanation:

Given :-

The ratio of the angles of a triangle is 2:3:7

To find :-

Find the measure of the smallest angle ?

Solution :-

Method-1:-

Given that

The ratio of the angles of a triangle = 2:3:7

Let they be 2X° , 3X° and 7X°

We know that

The sum of all the three angles in a triangle is 180°

=> 2X° + 3X° + 7X° = 180°

=> 12X° = 180°

=> X° = 180°/12

=> X° = 15°

So,

2X° = 2×15° = 30°

3X° = 3×15° = 45°

7X° = 7×15° = 105°

The smallest angle = 30°

Method-2:-

Given that

The ratio of the angles of a triangle = 2:3:7

Total parts = 2+3+7 = 12

We know that

The sum of all the three angles in a triangle is 180°

Total parts = 180°

=> 12 parts = 180°

Each part = 180°/12 = 15°

Smallest parts = 2

2 parts = 2×15° = 30°

The smallest angle = 30°

Answer:-

The smallest angle in a triangle = 30°

Used formulae:-

Angle Sum Property:-

• The sum of all the three angles in a triangle is 180°