document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1096896>Question 1096896</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Lines AB and CD are parallel to each other. Inside the lines AB and CD, there is a point P and an angle P consisted of segment XP and segment PY (XP and PY form an acute angle). The acute angle that XP and AB form is 35 degrees. The acute angle that PY and CD form is 42 degrees. What is the measure of angle P?\r<BR>\n" );
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document.write( "Sorry if this question is a bit unclear! If it's possible, can you also tell me how to make graphs in questions? Thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #711297 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=711297\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28450%2C300%2C-2%2C13%2C-1.5%2C8.5%2C%0D%0Aline%28-2%2C0%2C13%2C0%29%2Cline%28-2%2C7%2C13%2C7%29%2C%0D%0Aarrow%288%2C0%2C12%2C0%29%2Carrow%288%2C7%2C12%2C7%29%2C%0D%0Acircle%284.5%2C3.15%2C0.1%29%2Clocate%284.2%2C3.5%2CP%29%2C%0D%0Ared%28arc%2810%2C7%2C2%2C2%2C145%2C180%29%29%2Clocate%288.1%2C7.1%2Cred%2835%5Eo%29%29%2C%0D%0Ared%28arc%288%2C0%2C2%2C2%2C180%2C222%29%29%2Clocate%286.2%2C0.8%2Cred%2842%5Eo%29%29%2C%0D%0Aline%284.5%2C3.15%2C8%2C0%29%2Cline%284.5%2C3.15%2C10%2C7%29%2C%0D%0Alocate%289.8%2C7.5%2CX%29%2Clocate%287.9%2C0%2CY%29%2C%0D%0Acircle%28-1%2C0%2C0.1%29%2Ccircle%2811%2C0%2C0.1%29%2C%0D%0Acircle%28-0.3%2C7%2C0.1%29%2Ccircle%2812.5%2C7%2C0.1%29%2C%0D%0Alocate%2812.3%2C7.6%2CB%29%2Clocate%28-0.5%2C7.6%2CA%29%2C%0D%0Alocate%28-1.2%2C-0.1%2CC%29%2Clocate%2810.8%2C-0.1%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Let us extend segment PX until it meets line CD at point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28Z%29 ALIGN=MIDDLE  ALT=\"green%28Z%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28450%2C300%2C-2%2C13%2C-1.5%2C8.5%2C%0D%0Aline%28-2%2C0%2C13%2C0%29%2Cline%28-2%2C7%2C13%2C7%29%2C%0D%0Aarrow%288%2C0%2C12%2C0%29%2Carrow%288%2C7%2C12%2C7%29%2C%0D%0Acircle%284.5%2C3.15%2C0.1%29%2Clocate%284.2%2C3.5%2CP%29%2C%0D%0Ared%28arc%2810%2C7%2C2%2C2%2C145%2C180%29%29%2Clocate%288.1%2C7.1%2Cred%2835%5Eo%29%29%2C%0D%0Ared%28arc%288%2C0%2C2%2C2%2C180%2C222%29%29%2Clocate%286.2%2C0.8%2Cred%2842%5Eo%29%29%2C%0D%0Agreen%28line%280%2C0%2C10%2C7%29%29%2Clocate%28-0.1%2C0%2Cgreen%28Z%29%29%2C%0D%0Aline%284.5%2C3.15%2C8%2C0%29%2Cline%284.5%2C3.15%2C10%2C7%29%2C%0D%0Alocate%289.8%2C7.5%2CX%29%2Clocate%287.9%2C0%2CY%29%2C%0D%0Acircle%28-1%2C0%2C0.1%29%2Ccircle%2811%2C0%2C0.1%29%2C%0D%0Acircle%28-0.3%2C7%2C0.1%29%2Ccircle%2812.5%2C7%2C0.1%29%2C%0D%0Alocate%2812.3%2C7.6%2CB%29%2Clocate%28-0.5%2C7.6%2CA%29%2C%0D%0Alocate%28-1.2%2C-0.1%2CC%29%2Clocate%2810.8%2C-0.1%2CD%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PYC ALIGN=MIDDLE  ALT=\"PYC\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same angle as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PYZ ALIGN=MIDDLE  ALT=\"PYZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just called by a different name),<BR>\n" );
document.write( "and measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=42%5Eo ALIGN=MIDDLE  ALT=\"42%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AXP ALIGN=MIDDLE  ALT=\"AXP\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the same angle as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AXZ ALIGN=MIDDLE  ALT=\"AXZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just called by a different name),<BR>\n" );
document.write( "and measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%5Eo ALIGN=MIDDLE  ALT=\"35%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XZD ALIGN=MIDDLE  ALT=\"XZD\"   DISABLED_style= \"max-width:90%; height:auto;\" > is congruent to angle as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=AXZ ALIGN=MIDDLE  ALT=\"AXZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because they are alternate interior angles.<BR>\n" );
document.write( "So, angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XZD=PZY ALIGN=MIDDLE  ALT=\"XZD=PZY\"   DISABLED_style= \"max-width:90%; height:auto;\" > measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%5Eo ALIGN=MIDDLE  ALT=\"35%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > too.<BR>\n" );
document.write( "The angle at P, angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XPY ALIGN=MIDDLE  ALT=\"XPY\"   DISABLED_style= \"max-width:90%; height:auto;\" > is an exterior angle to traingle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PYZ ALIGN=MIDDLE  ALT=\"PYZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and as all exterior angles to a triangle,<BR>\n" );
document.write( "its measure is the sum of the measures of the non-adjacent interior angles of the triangle<BR>\n" );
document.write( "(in this case angles <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PZY ALIGN=MIDDLE  ALT=\"PZY\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=PYZ ALIGN=MIDDLE  ALT=\"PYZ\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
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document.write( "So, the measure of angle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=XPY ALIGN=MIDDLE  ALT=\"XPY\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35%5Eo%2B42%5Eo=highlight%2877%5Eo%29 ALIGN=MIDDLE  ALT=\"35%5Eo%2B42%5Eo=highlight%2877%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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