document.write( "Question 417934: In a diagram, O is the center of circle ABCD and ∠DAB=67°. Calculate the value of (i)∠DOB, (ii)∠DCB \n" ); document.write( "
Algebra.Com's Answer #292673 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Angle DAB is an inscribed angle subtending arc DCB.\r\n" );
document.write( "Angle DOB is a central angle also subtending arc DCB.\r\n" );
document.write( "\r\n" );
document.write( "An arc subtended by an inscribed angle has the measure of \r\n" );
document.write( "twice the measure of the inscribed angle, thus arc DCB has measure\r\n" );
document.write( "2×67° or 134°.\r\n" );
document.write( "\r\n" );
document.write( "A central angle has the same measure as the measure of its\r\n" );
document.write( "subtended arc, thus angle DOB also has measure 134°.\r\n" );
document.write( "\r\n" );
document.write( "Angle DCB is an inscribed angle subtending major arc DAB.\r\n" );
document.write( "Since a complete circle is an arc of 360°, the measure of\r\n" );
document.write( "arc DAB is 360°-134° or 226°.\r\n" );
document.write( "\r\n" );
document.write( "The measure of an inscribed angle is 1/2 the measure of its\r\n" );
document.write( "subtended arc, so angle DCB has measure 1/2 × 226° or 113°.\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "
\n" );