Question

) The three angles of a triangle are in the ratio 1:2:3.Find the measure of smallest angle​

Answer 1

Question:-

The three angles of a triangle are in the ratio 1:2:3.Find the measure of smallest angle

Answer:-

• The smallest angle is 30°

To find:-

• Smallest angle

Solution:-

• Ratio = 1:2:3

Let,

• First angle = x
• Second angle = 2x
• Third angle = 3x

As we know,

• Sum of all angles of triangle = 180°

According to question,

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: x + 2x + 3x = 180 \degree}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: 6x = 180 \degree}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: x = \frac{180}{6} }$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: \: x = 30 \degree}$

• The value of x is 30°

Now,

• First angle = x = 30°
• Second angle = 2x = 60°
• Third angle = 3x = 90°

Hence,

The smallest angle is 30°