The value of x is 34, m∠S = 38° and m∠T = 111°.
Solution:
Given RST is a triangle.
m∠R = 31°, m∠S = (x + 4)° and m∠T = (3x + 9)°
Sum of the angles of a triangle = 180°
m∠R + m∠S + m∠T = 180°
⇒ 31° + (x + 4)° + (3x + 9)° = 180°
⇒ 31° + x° + 4° + 3x° + 9° = 180°
⇒ 44° + 4x° = 180°
Subtract 44° from both sides.
⇒ 4x° = 136°
Divide by 4 on both sides.
⇒ x° = 34°
⇒ x = 34
m∠S = (x + 4)°
= (34 + 4)°
m∠S = 38°
m∠T = (3x + 9)°
= (3(34) + 9)°
m∠T = 111°
Hence the value of x is 34, m∠S = 38° and m∠T = 111°.
