document.write( "Question 1199998: In the diagram, Angle A = 40° while BD and CD are the bisectors of
\n" ); document.write( "angles EBC and FCB respectively. Find the measure of angle D. \r
\n" ); document.write( "\n" ); document.write( "https://ibb.co/2My3RKd\r
\n" ); document.write( "\n" ); document.write( "Thanks! \n" ); document.write( "

Algebra.Com's Answer #834019 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In the diagram, Angle A = 40° while BD and CD are the bisectors of
\n" ); document.write( "angles EBC and FCB respectively. Find the measure of angle D.
\n" ); document.write( "https://ibb.co/2My3RKd
\n" ); document.write( "Thanks!
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "The sum of angles ABC and ACB is 180° - 40° = 140°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The angles EBC and FCB are outer angles of the triangle ABC to angles ABC and ACB, respectively.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Therefore, the sum of angles EBC and FCB is \r\n" );
document.write( "\r\n" );
document.write( "    (180°- < ABC) + (180° - < FCB) = 360° - 140° = 220°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Angles CBD and DCB are halves of angles EBC and FCB;\r\n" );
document.write( "\r\n" );
document.write( "therefore, < CBD + < DCB = 220°/2 = 110°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "It implies that angle D is  180° - 110° = 70°.    ANSWER\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "ANSWER.  The angle D measure is 70°.\r\n" );
document.write( "

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

\n" );