Question

#2 is the one I need help with

Answer 1

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:

`m\angle 1= \frac {1}{2} * 3x\\\\</p><p>\therefore m\angle 1= \frac {1}{2} * 120°\\\\</p><p>\huge \red {\boxed {\therefore m\angle 1= 60°}}`

By tangent secant theorem:

`m\angle 2 = \frac {1}{2} * 3x\\\\</p><p>\therefore m\angle 2 = \frac {1}{2} * 120°\\\\</p><p>\huge \purple {\boxed {\therefore m\angle 2 = 60°}}`

Since, measure of central angle is equal to the measure of its corresponding minor arc.

`m\angle 3 = 3x\\\\</p><p>\huge \pink {\boxed {\therefore m\angle 3 = 120°}}`

By angle sum Postulate of a triangle:

`m\angle 3 + 2 m\angle 4 = 180°\\\\</p><p>120° + 2 m\angle 4 = 180° \\\\</p><p>2 m\angle 4 = 180°- 120° \\\\</p><p>2 m\angle 4 = 60° \\\\</p><p>m\angle 4 = \frac {60°}{2} \\\\</p><p>\huge \orange {\boxed {m\angle 4 =30°}}`