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avatar+1442 

In the diagram shown, PC is tangent to the circle and PD is the angle bisector of CPE. If arc CD is 70 degrees, arc DE is 30 degrees, and DQE = 40 degrees, then determine arc AE, in degrees.

 

Thanks!

AnonymousConfusedGuy  Apr 24, 2018
 #1
avatar+91046 
+1

Because CE  is a chord meeting a tangent, the measure of the angle supplemental  to angle PCQ =

 

(1/2) ( m arc CDE)  =   (1/2) (m arc CD + m arc DE ) = (1/2) ( 70 + 30)  =  50°

 

So....angle  PCQ  =  180 - 50  =  130°

 

And angle  CQP is vertical to angle DQE  =  40°  

 

So....in triangle PCQ, angle PCQ  = 130  and angle CQP = 40

 

So  angle CPQ  =  180 - 130 - 40  =  10°

 

And angle  QPE  equals this  = 10°

 

And angle PQE is supplemental to  angle DQE  = 140°

 

So...in triangle PQE,  angle QEP  = 180 - 140 - 10  = 30°

 

So m arc CA  is twice this  = 60°

 

So   m arc AE  =  360 - m arc DE - m arc CD  - m arc CA  =

 

360  - 30 - 70 - 60  =

 

360  - 160  =

 

200°

 

This doesn't  "look " to be correct......[ I don't think I made any mistakes, but maybe I did !!!!]

 

 

cool cool cool

CPhill  Apr 25, 2018
 #2
avatar+1442 
+2

You were right thanks so much!

AnonymousConfusedGuy  Apr 25, 2018

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