Question

Of the three angles of a triangle, one is twice the smallest and another is three times

the smallest. Find the angles.​

Answer 1

GIVEN :

• The three angles of a triangle, one is twice the smallest and another is three times the smallest.

TO FIND :

• The angles = ?

SOLUTION :

• Let the triangle (smallest angle) be x

• Second angle be 2x

• And third angle be 3x

★ By angle sum property we get,

➨ x + 2x + 3x = 180

➨ 6x = 180

➨ x = 180/6

➨ x = 30°

Now, substituting the value of x in other angles we get :

Second angle = 2x = 2 × 30 = 60°

Third angle = 3x = 3 × 30 = 90°

Therefore, the angles are 30°, 60° and 90°.

Answer 2

◘ Given ◘

Of the three angles of a triangle, one is twice the smallest and another is three times the smallest.

If the angles are x, y and z, then let the smallest angle be z.

• x = 2z

• y = 3z

◘ To Find ◘

The value of all the angles.

◘ Solution ◘

In a triangle, we know,

x + y + z = 180°   (By Angle Sum Property)

✍ According to the given conditions,

2z + 3z + z = 180°

⟶ 6z = 180°

⟶ z = 180/6

⟶ z = 30°

________________

Now, the angles are :-

z = 30°

x = 2z = 2 × 30 = 60°

y = 3z = 3 × 30 = 90°