+0  
 
-1
67
1
avatar+17 

In rectangle EFGH, EH = 3 and EF = 4. Let M be the midpoint of \(\overline{EF}\), and let be a X point such that MH = MX and \(\angle MHX = 72^\circ\), as shown below. Find angle XGH, in degrees.

 

 Apr 10, 2020
 #1
avatar+111329 
+4

The  key to this problem  may  not  be obvious, at first

 

With M as a center, construct a circle  with radius, MH

 

Note  that  MH  = MG  = MX

 

So.....this circle will  pass through H, X and G

 

Since MH = MX,  then  in triangle MHX, angle MHX  = angle MXH  = 72

 

So  angle  HMX  =  180  - 72 - 72  =  36

 

So angle HMX  is  a central angle  in the  circle

 

And angle  HGX  is an inscribed angle which intercepts the same arc as angle HMX

 

So....it  has (1/2)  the measure  of angle HMX  = (1/2) (36)  =  18°

 

cool cool cool

 Apr 10, 2020

27 Online Users

avatar
avatar
avatar