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5.The measures of the angles of triangle ABC are in the ratio 2:4:9. What are the measures of the angles.

Respuesta :

Given :

  • The measures of the angles of triangle ABC are in the ratio 2:4:9.

To Find :

  • The measures of the angles.

Solution :

  • Let the angles of the triangle be 2x, 4x and 9x

We know that the sum of the angles of the triangle is 180°

So,

⠀⠀2x + 4x + 9x = 180°

➺ 15x ⠀⠀⠀⠀⠀⠀= 180°

➺ x ⠀⠀⠀⠀⠀⠀⠀= 180°/15

➺ x ⠀⠀⠀⠀⠀⠀⠀= 12°

⠀

So, The measure of the three angles are :

  • 2x = 2 × 12° = 24°
  • 4x = 4 × 12° = 48°
  • 9x = 9 × 12° = 108°

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