circle, angle

**dodoldotkom** · March 28th 2012, 05:26 AM

Hi,

I have this problem:

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

Thank you so much for your help.

**Soroban** · March 28th 2012, 06:28 AM

Hello, dodoldotkom!

I have this problem:

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

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

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

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

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

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

**dodoldotkom** · March 28th 2012, 06:36 AM

Thank you so much you are truly amazing!

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