# circle, angle

• Mar 28th 2012, 05:26 AM
dodoldotkom
circle, angle
Hi,

I have this problem:
Attachment 23447

AC = Diameter
DBC = 30 degree
BDC = 35 degree
AED = ? degree

How can I find AED ?

I have try to find the other angles but still can't find AED
Attachment 23448

Thank you so much for your help.
• Mar 28th 2012, 06:28 AM
Soroban
Re: circle, angle
Hello, dodoldotkom!

Quote:

I have this problem:
Attachment 23447

AC = Diameter
DBC = 30 degree
BDC = 35 degree
AED = ? degree

$\displaystyle AC\text{ is a diameter.}$
$\displaystyle \text{Hence: }\:\text{arc}(ABC) \,=\,\text{arc}(ADC) \,=\,180^o$

$\displaystyle \angle DBC = 30^o \quad\Rightarrow\quad \text{arc}(DC) = 60^o$

. . $\displaystyle \text{arc}(AD) = 120^o \quad\Rightarrow\quad \angle ACD = 60^o$

$\displaystyle \text{In }\Delta ECD: \:\angle ECD = 60^o,\;\angle EDC = 35^o \quad\Rightarrow\quad \angle DEC = 85^o$

$\displaystyle \text{Therefore: }\:\angle AED = 95^o$

• Mar 28th 2012, 06:36 AM
dodoldotkom
Re: circle, angle
Thank you so much you are truly amazing!