Step-by-step explanation:
By arc sum Postulate of a circle:
2 x + 3x + 4x = 360°
9x = 360°
x = 360°/9
x = 40°
3x = 3* 40° = 120°
By inscribed angle theorem:
[tex] m\angle 1= \frac {1}{2} \times 3x\\\\
\therefore m\angle 1= \frac {1}{2} \times 120°\\\\
\huge \red {\boxed {\therefore m\angle 1= 60°}} [/tex]
By tangent secant theorem:
[tex] m\angle 2 = \frac {1}{2} \times 3x\\\\
\therefore m\angle 2 = \frac {1}{2} \times 120°\\\\
\huge \purple {\boxed {\therefore m\angle 2 = 60°}} [/tex]
Since, measure of central angle is equal to the measure of its corresponding minor arc.
[tex] m\angle 3 = 3x\\\\
\huge \pink {\boxed {\therefore m\angle 3 = 120°}} [/tex]
By angle sum Postulate of a triangle:
[tex] m\angle 3 + 2 m\angle 4 = 180°\\\\
120° + 2 m\angle 4 = 180° \\\\
2 m\angle 4 = 180°- 120° \\\\
2 m\angle 4 = 60° \\\\
m\angle 4 = \frac {60°}{2} \\\\
\huge \orange {\boxed {m\angle 4 =30°}}[/tex]
