Question

cho tam giac ABC ve tia phan giac AD tai A biet ADB=80 B=3/2C tinh cac goc cua tam giac ABC

Answer 1

\(\widehat{ADC}=180^0-80^0=100^0\)

Ta có: \(\widehat{ADB}+\widehat{B}+\widehat{BAD}=\widehat{ADC}+\widehat{C}+\widehat{CAD}\)

mà \(\widehat{BAD}=\widehat{CAD}\)

nên \(\widehat{ADB}+\widehat{B}=\widehat{ADC}+\widehat{C}\)

=>\(\widehat{B}-\widehat{C}=100^0-80^0=20^0\)

=>\(\dfrac{3}{2}\widehat{C}-\widehat{C}=20^0\)

=>\(\widehat{C}=40^0\)

\(\widehat{B}=\dfrac{3}{2}\cdot40^0=60^0\)

\(\widehat{BAC}=180^0-40^0-60^0=80^0\)