Question

In the figure 1.75 $\angle$BAC = 75$°$, $\angle$ABC = 35$°$. Find the measures of $\angle$BAZ, $\angle$CBX, and $\angle$ACY.

Answer 1

Given:
$$\begin{gathered} \angle \mathrm{BAC}=75° \\ \angle \mathrm{ABC}=35° \end{gathered}$$


$$\begin{gathered} \mathrm{Here},\angle \mathrm{BAZ}+\angle \mathrm{BAC}=180°(\mathrm{Linear}\mathrm{pair}) \\ \Rightarrow \angle \mathrm{BAZ}+75°=180°\left(\mathrm{Given}\right) \\ \Rightarrow \angle \mathrm{BAZ}=105° \\ \mathrm{Similarly},\angle \mathrm{ABC}+\angle \mathrm{CBX}=180°(\mathrm{Linear}\mathrm{pair}) \\ \Rightarrow 35°+\angle \mathrm{CBX}=180°\left(\mathrm{Given}\right) \\ \Rightarrow \angle \mathrm{CBX}=145° \\ \mathrm{Now},\angle \mathrm{ACY}=\angle \mathrm{BAC}+\angle \mathrm{ABC}(\mathrm{Exterior}\mathrm{angle}\mathrm{property}) \\ \therefore \angle \mathrm{ACY}=75°+35°=110° \end{gathered}$$