1. Cho Hình 3.36, biết MN // BC

1. Do MN // BC nên $\widehat{AMN}=\widehat{ABC}$ (hai góc đồng vị) nên $\widehat{AMN}=60°.$

Do $\widehat{AMN}$ và $\widehat{BMN}$ là hai góc kề bù nên $\widehat{AMN}+\widehat{BMN}=180°$

Hay $\widehat{BMN}+60°=180°$ do đó $\widehat{BMN}=180°-60°=120°.$

Do $\widehat{ANM}$ và $\widehat{MNC}$ là hai góc kề bù nên $\widehat{ANM}+\widehat{MNC}=180°$

Hay $\widehat{ANM}+150°=180°$ do đó $\widehat{ANM}=180°-150°=30°.$

Do MN // BC nên $\widehat{ANM}=\widehat{ACB}$ (hai góc đồng vị).

Do đó $\widehat{ACB}=30°.$

Vậy $\widehat{BMN}=120°;\widehat{ACB}=30°.$

2.

Do $xx\text{'}\perp zz\text{'}$ nên $\widehat{x^{\text{'}}AB}=90°.$

Do $xx\text{'}//yy\text{'}$ nên $\widehat{x^{\text{'}}AB}=\widehat{ABy}.$

Do đó $\widehat{ABy}=90°.$

Vậy $zz\text{'}\perp yy\text{'}.$