Cho hình vẽ bên, biết AE // BC

- Hướng dẫn giải

a) Vì $\text{AE // BC}$ nên $\widehat{\text{ABC}}=\widehat{\text{EAB}}$ (hai góc so le trong)

mà $\widehat{\text{EAB}}={70}^{\circ }$ nên $\widehat{\text{ABC}}={70}^{\circ }$

b) Vì $\text{AE // BC}$ nên $\widehat{\text{EAC}}+\widehat{\text{ACB}}={180}^{\circ }$

hay $\widehat{\text{EAB}}+\widehat{\text{BAC}}+\widehat{\text{ACB}}={180}^{\circ }$ mà $\widehat{\text{EAB}}={70}^{\circ }$và $\widehat{\text{ACB}}={75}^{\circ }$

$\Rightarrow {70}^{\circ }+\widehat{\text{ABC}}+{75}^{\circ }={180}^{\circ }$

$\Rightarrow \widehat{\text{BAC}}={180}^{\circ }-({70}^{\circ }+{75}^{\circ })$

$\Rightarrow \widehat{\text{BAC}}={180}^{\circ }-{145}^{\circ }$

$\Rightarrow \widehat{\text{BAC}}={35}^{\circ }$