document.write( "Question 1025582: In isosceles triangle AB$ (with AB = AC), point D lies on AB such that CD = CB. If angle ADC = 115 degrees, what is angle ACD (in degrees)?
\n" ); document.write( " image: http://classroom.artofproblemsolving.com/Classes/IntroGeom/Images/480402815.gif \n" ); document.write( "

Algebra.Com's Answer #640854 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "In isosceles triangle AB$ (with AB = AC), point D lies on AB such that CD = CB. If angle ADC = 115 degrees, what is angle ACD (in degrees)?
\n" ); document.write( " image: http://classroom.artofproblemsolving.com/Classes/IntroGeom/Images/480402815.gif
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "1.  angle(CDB) = 180° - angle(ADC) = 180° - 115° = 65° (as a complementary angle).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "2.  angle(CBD) = angle(CDB) = 65° as the triangle CBD is isosceles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "3.  angle(ACB) = angle(ABC) = 65° as the triangle ABC is isoceles.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "4.  From the triangle ABC, angle(A) = 180° - (65°+65°) = 50°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "5.  From the triangle ADC, angle(ACD) = 180° - (115°+50°) = 15°.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The problem is solved.\r\n" );
document.write( "

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

\n" );