Answer
The value of x = 14
m∠T = 65°
m∠S = 30°
m∠R = 85°
Step-by-step 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°