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In the diagram below, we have \(\overline{AB}\parallel\overline{CD}\), \(QP = QR\), \(\angle BPQ = x^\circ + 100^\circ\), and \(\angle APR = x^\circ\). Find x.

 Mar 15, 2020
 #1
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Since QP = QR, 2x + 100 = 180.  Then x = 40.

 Mar 15, 2020
 #2
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BPQ + QPR + APR = 180   

so  x+100+QPR+x = 180 

or  2x + QPR = 80 ...(1)

 

QRP = APR 

QPR = QRP (because triangle QRP is isosceles with QR = QP) hence QRP = APR = x

use this in (1) to get:

 

2x + x  = 80

 

3x = 80

 

x = 80/3 

 Mar 15, 2020

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