document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209480>Question 1209480</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The center of the circle is O, angle TQR = 46 degrees and angle QTO = 51 degrees.<BR>\n" );
document.write( "Find the measure of angle RPO.\r<BR>\n" );
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document.write( "Link to graph: https://ibb.co/bmnmVgb </SPAN>\n" );
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document.write( "The measure of angle TQR is given as 46 degrees, so the measure of angle TQP is 180-46 = 134 degrees.<br><BR>\n" );
document.write( "That means the measure of major arc PT is 2*134 = 268 degrees.<br><BR>\n" );
document.write( "That in turn means the measure of minor arc PT is 360-368 = 92 degrees.<br><BR>\n" );
document.write( "And since central angle POT cuts off minor arc PT, the measure of angle POT is 92 degrees.<br><BR>\n" );
document.write( "The measure of angle QTO was given as 51 degrees.<br><BR>\n" );
document.write( "Now we have the measures of three of the four angles in quadrilateral POTQ, so the measure of angle RPO (= measure of angle QPO) is 360-(134+51+92) = 83 degrees.<br><BR>\n" );
document.write( "ANSWER: 83 degrees<br><BR>\n" );
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