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Let $\angle ABC = x$, $\angle BCD = 2x$, and $\angle CDE = 3x$. If $\angle BAE$ is $90^{\circ}$, what is the angle of $\angle ABC$ in degrees?

 

 Jan 8, 2021
 #1
avatar+861 
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Let ∠ABC = x, ∠BCD = 2x , and ∠CDE = 3x. If ∠BAE is 90º, what is the measure of ∠ABC in degrees?

 

https://web2.0calc.com/questions/please-help_54385

 

(Answered brilliantly by thelizzybeth, Jun 25, 2020)

 Jan 8, 2021
edited by Guest  Jan 8, 2021
edited by jugoslav  Jan 8, 2021
 #2
avatar+114361 
+2

 

arc BD  = 4x 

 

And angle  DEA will intercept  an   arc of 90 +  BD =   90 + 4x

So...its measure  = (90 +  4x)   / 2

And angle CDE  = 3x

 

Let BC  and DC  intersect  AE  at   F and G respectively

 

Angle   FGC   = 180 - [ angle  DEA  + angle CDE ] = 180 -  [(90 + 4x)  /2  +  3x]

Angle  GFC  = 90 - BCA  = 90 - x

Angle BCD  =2x

 

So  ....in triangle  GFC  we  that

 

Angle FGC  + Angle  BCD  + Angle  GFC   =180

 

 

180 - [ (90 + 4x)  / 2  +  3x ]   + 2x + [   90 - x ]  = 180

 

 

180 - 45  - 2x   -  3x  +  2x  +  90  - x  = 180

 

 -4x  + 45   = 0

 

4x  = 45

 

x  = 45/4 =     11.25° = ABC

 

 

 

cool cool cool

 Jan 8, 2021
edited by CPhill  Jan 8, 2021

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