Question

I would like some help thank you :)

Answer 1

Answer:

$\angle AE = 32^{\circ}$

$\angle EAD = 212^{\circ}$

$\angle BE = 133^{\circ}$

$\angle BCE = 227^{\circ}$

$\angle AED = 180^{\circ}$

$\angle BD = 79^{\circ}$

Step-by-step explanation:

The central angle of a circle is equal to 360º, whose formula in this case is:

$\angle AB + \angle BC + \angle CD + \angle DE + \angle EA = 360^{\circ}$

In addition, the following conditions are known from figure:

$\angle BC = 47^{\circ}$, $\angle DE = 148^{\circ}$

$\angle DE + \angle EA = 180^{\circ}$

$\angle CD + \angle DE = 180^{\circ}$

$\angle AB + \angle BC + \angle CD = 180^{\circ}$

Now, the system of equations is now solved:

$\angle EA = 180^{\circ}-\angle DE$

$\angle EA = 180^{\circ}-148^{\circ}$

$\angle EA = 32^{\circ}$

$\angle CD = 180^{\circ}-\angle DE$

$\angle CD = 180^{\circ}-148^{\circ}$

$\angle CD = 32^{\circ}$

$\angle AB = 180^{\circ} - \angle BC - \angle CD$

$\angle AB = 180^{\circ}-47^{\circ}-32^{\circ}$

$\angle AB = 101^{\circ}$

The answers are described herein:

$\angle AE = 32^{\circ}$

$\angle EAD = 212^{\circ}$

$\angle BE = 133^{\circ}$

$\angle BCE = 227^{\circ}$

$\angle AED = 180^{\circ}$

$\angle BD = 79^{\circ}$