Question

the measures of three angles of a triangle are in ration 3:4:5. Find the measures of the three angles​

Answer 1

Question:-

the measures of three angles of a triangle are in ration 3:4:5. Find the measures of the three angles

Answer:-

• The angles of triangle are 45°,60° and 75°.

To find:-

• All angles of triangle

Solution:-

• Ratio of angles = 3:4:5

Let,

• First angle = 3x
• Second angle = 4x
• Third angle = 5x

As we know,

• Sum of all angles of triangle = 180°

According to question,

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: 3x + 4x + 5x = 180 \degree}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: 12x =180 \degree}$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: x = \frac{180}{12} }$

$\large{ \rm : \implies \: \: \: \: \: \: \: \: \: x = 15 \degree}$

Now,

• First angle = 3x = 45°
• Second angle = 4x = 60°
• Third angle = 5x = 75°

Hence,

The angles of triangle are 45°,60° and 75°.

Answer 2

Given:

• The angles of triangle are in the ratio 3 : 4 : 5.

To Find:

• Those angles

Solution:

Put x in the ratio

Now, angles are

• 3x
• 4x
• 5x

★As we know:

• Sum of measure of triangle is 180°

★According to the question:

→ 3x + 4x + 5x = 180°

→ 7x + 5x = 180°

→ 12x = 180°

→ x = 180/12

→ x = 15

Put the value x in the ratio

• 3x = 3 × 15 = 45°
• 4x = 4 × 15 = 60°
• 5x = 5 × 15 = 75°

Hence,

• All angles are 45°, 60° and 70°.