如图,已知△ABC中,AB=AC,D在BC上,E在AC上,且AD=AE,∠BAD=46°,那么∠CDE的度数为_.
问题描述:
如图,已知△ABC中,AB=AC,D在BC上,E在AC上,且AD=AE,∠BAD=46°,那么∠CDE的度数为______.
答
设∠DAC=x°,
∵AB=AC,
∴∠B=
=(67-180°−(46+x)° 2
)°,x 2
∴∠ADC=46°+(67-
)°=(113-x 2
)°,x 2
∵AD=AE,
∴∠ADE=
=(90-180°−x° 2
)°,x 2
∴∠CDE=(113-
)°-(90-x 2
)°=23°,x 2
故答案为:23°.