+0  
 
0
42
1
avatar

Segment $BD$ and $AE$ intersect at $C$, as shown, $AB=BC=CD=CE$, and $\angle A = \frac 32 \angle B$. What is the degree measure of $\angle D$?

 

 Mar 18, 2021
 #1
avatar+118015 
+1

Since  AB  = BC....then  angles  BAC   and  BCA  are equal

 

Call angle ABC = x

Then  angles  BAC  and  BCA = (3/2) x

 

So   

(3/2)x  + (3/2) x  +  x  =180

3x  + x  =180

4x = 180

x = 180 / 4 =  45°

 

So angle  BCA = (3/2) 45  =  67.5 =  angle ECD

 

And  because  CD = CE....then angles CED  and CDE  are equal

 

So

 

Angle CDE    =   (180  - 67.5)  /  2  =  56.25°   =   "angle D"

 

 

cool cool cool

 Mar 18, 2021

63 Online Users

avatar
avatar
avatar
avatar
avatar