We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
308
7
avatar+4094 

 

 

In the diagram, if  \(\triangle ABC\) and \(\triangle PQR\) are equilateral, then what is the measure of 

\(\angle CXY\) in degrees?

 

 

https://latex.artofproblemsolving.com/c/5/a/c5a3159832bd8c1395bc179beaf94b1c58a2e9eb.png

 Feb 20, 2018
 #1
avatar+18049 
+2

See diagram below

 Feb 20, 2018
 #3
avatar+4094 
+2

Great diagram! Thanks so much, EP!

tertre  Feb 20, 2018
 #2
avatar+99580 
+2

 

 

Angle YBP  = 180  - 65 - 60  = 55°

 

Angle BYP  =  180  - 75 - 60 = 45°

 

So

 

Angle BYP  =  180  - 55 - 45  = 80°

 

And Angle CYX is a vertical  angle to BYP  ....so it = 80°

 

So.... CXY  =  180  - 60  - 80   =   40°

 

 

cool cool cool

 Feb 20, 2018
 #4
avatar+4094 
+2

Amazing Explanation, CPhill! Great job!

tertre  Feb 20, 2018
 #5
avatar+99580 
+1

Thanks, tertre.....!!!

 

 

 

cool cool cool

CPhill  Feb 20, 2018
 #6
avatar+18049 
+1

Glad it helped , Tertre......waiting to see what the answer is to your red/white ball question to see if I got it correct!

 Feb 20, 2018
 #7
avatar+182 
+3

Let's see if I can solve this:

Since \(\triangle ABC\) and \(\triangle PQR\) are equilateral, then \(\angle ABC=\angle ACB=\angle RPQ=60^\circ\).

Therefore, \(\angle YBP = 180^\circ-65^\circ-60^\circ=55^\circ\)  and \(\angle YPB = 180^\circ-75^\circ-60^\circ=45^\circ\) .

In \(\triangle BYP\), we have \(\angle BYP = 180^\circ - \angle YBP - \angle YPB = 180^\circ - 55^\circ-45^\circ=80^\circ\).

Since \(\angle XYC = \angle BYP\) , then \(\angle XYC=80^\circ\).

In \(\triangle CXY\), we have \(\angle CXY = 180^\circ - 60^\circ - 80^\circ = 40^\circ\).

So our final answer is \(\boxed{40}\) degrees.

 Feb 20, 2018

2 Online Users