Question

the angle of a triangle are in the ratio 3:4:5 find the measure of an angle a,b,c​

Answer 1

Given :-

• Ratios of angles of the Triangle are 3:4:5.

To Find :-

• Measure of each angle of the Triangle.

Solution :-

Let First angle be 3x

Let Second angle be 4x

Let Third angle be 5x

Angle Sum Property of Triangle is 180°

According to the Question :

⇒ ∠ a + ∠ b + ∠ c = 180

⇒ 3x + 4x + 5x = 180

⇒ 7x + 5x = 180

⇒ 12x = 180

⇒ x = 180/12

⇒ x = 15

________________

Verification :-

⇒ ∠ a + ∠ b + ∠ c = 180

⇒ 3 × 15 + 4 × 15 + 5 × 15 = 180

⇒ 45 + 60 + 75 = 180

⇒ 105 + 75 = 180

⇒ 180 = 180

Hence Verified

________________

Measures of Angles :

First Angle = 3x = 3 × 15 = 45°

Second Angle = 4x = 4 × 15 = 60°

Third Angle = 5x = 5 × 15 = 75°

________________