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Answer

The value of x = 14

m∠T = 65°

m∠S = 30°

m∠R = 85°

Explanation

From the given ΔRST,

m∠T + m∠S + m∠R = 180° (Sum of angles in a triangle)

m∠T = (4x + 9)°, m∠S = (2x + 2)° and m∠R = (7x - 13)°

⇒(4x + 9)° + (2x + 2)° + (7x - 13)° = 180°

Grouping the terms, we have

4x + 2x + 7x + 9 + 2 - 13 = 180°

13x - 2 = 180°

13x = 180 + 2

13x = 182

Divide both sides by 13

13x/13 = 182/13

x = 14

Therefore,

m∠T = (4x + 9)° = (4(14) + 9)° = (56 + 9)° = 65°

m∠S = (2x + 2)° = (2(14) + 2)° = (28 + 2)° = 30°

m∠R = (7x - 13)° = (7(14) - 13)° = (98 - 13)° = 85°

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