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Measures of angles are X = 102° and Y = 78°

Step-by-step explanation:

  • Step 1: Let ∠X = 24 + Y. As they are supplementary angles, ∠X + ∠Y = 180°

⇒ 24 + Y + Y = 180

⇒ 2Y = 180 - 24 = 156

⇒ Y = 156/2 = 78°

  • Step 2: Find measure of X

⇒ X = 24 + Y = 24 + 78 = 102°