Question

solve plzzz .??????????

Answer 1

Answer: 50°

Step-by-step explanation:

See the attachment for solution and sorry for my poor drawing

Answer 2

In triangle HIJ,



$\alpha + \beta + \theta = 180° \\ \alpha + \beta = 180° - \theta$
Since,
Exterior angle of triangle equals the sum of two interior opposite angles.

Therefore,

In triangle ABG,

Angle A + Angle G = Angle FBC
$\alpha + \beta = \text{angle} FBC \\ \text{angle} FBC = 180° - \theta$
Now
Angle FED + Reflex Angle FED = 360°

150° + Reflex Angle FED = 360°

Reflex Angle FED = 210°

Also,
Angle BFE + Angle GFE = 180°
$\text{Angle} BFE + \theta = 180° \\ \text{Angle} BFE = 180° - \theta$

And,

$\text{Angle} BCD = \theta$
as they are vertically opposite.


Now we have all the angles.

Angle BCD + Angle CDE + Reflex Angle FED + Angle BFE + Angle FBC = 540° (As it is 5 sided polygon so sum of angles equals (5-2)×180° = 540°)

Therefore,

$\theta + 20° + 210° + 180° - \theta+ 180° - \theta = 540° \\ 590° - \theta= 540° \\ \boxed{\theta= 50° }$