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Measures of the angles are 24°, 48° and 108°

Step-by-step explanation:

  • Step 1: Given ratio = 2:4:9. Sum of angles of triangle = 180°

Let angles be 2x, 4x and 9x.

⇒ 2x + 4x + 9x = 180

⇒ 15x = 180

⇒ x = 180/15 = 12

  • Step 2: Find angles.

2x = 24°, 4x = 48° and 9x = 108°

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