Question

The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is

विकल्प

• 30°

• 60°

• 90°

• 120°

Answer 1

90°
The ratio of the angles of a triangle is 3:1:2

Let x be any number such that the three angles are (3x)°, (1x)°, and (2x)°.
We know, the sum of the angles of a triangle is 180°.
3x + 1x + 2x= 180
⇒ 6x = 180
​ ⇒ x = `180/6` = 30

∴ (3x)°= (3 ​× 30)° = 90°
(1x)° = (1​ × 30)° = 30°
​(2x)° = (2 × 30)° = 60°
The measure of the largest angle is 90°​.