Question

if the exterior angle of a triangle is 60° and the interior opposite angles are in the ratio 1 is to 3 then the angles of the triangle are​

Answer 1

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Answer 2

Given :

• Exterior angle of a triangle is 60°.
• Ratio of the interior opposite 1 : 3.

To Find :

The angles of the triangle.

Solution :

Analysis :

Here we have to use the concept of exterior angle.

Explanation :

Let the common ratio be “x”.

• x
• 3x

We know that the sum of two opposite interior angles is equal to the exterior angle.

☯ According to the question,

⇒ x + 3x = 60

⇒ 4x = 60

⇒ x = 60/4

⇒ x = 15

∴ x = 15.

The angles :

• x = 15°
• 3x = 3 × 15 = 45°

The angles of the triangle are 15°, 45°.

Verification

LHS :

• Putting x = 15,

⇒ 15 + 3(15)

⇒ 15 + 45

⇒ 60 = 60

∴ 60°.

RHS :

∴ 60°.

∴ LHS = RHS.

• Hence verified.