+0  
 
0
36
1
avatar

Trapezoid HGFE is inscribed in a circle, with EF || GH. If arc GH is 70 degrees, arc EH is x^2 - 2x degrees, and arc FG is 65 - 3x degrees, where x > 0, find arc EPF, in degrees.  Round your answer to the nearest tenth.

 

 Jun 29, 2022
 #1
avatar+124526 
+1

Since  EF ll GH, then arcs  EH and FG are equal  .....so....

 

 x^2 - 2x =  65 - 3x

 

x^2 + x - 65   =  0 

 

x ≈ 7.58

 

So   arc EH = arc FG =  65 - 3(7.58)  =  42.26°

 

Then arc EPF  = 

 

360 - 2 * arc EH  - arc  GH

 

360  - 2(42.26) - 70   ≈ 205.5° 

 

 

cool cool cool

 Jul 3, 2022

6 Online Users

avatar
avatar