in the figure, PQ // RS, angle PAB = 70 and ACS =100, FIND angle ABC, BAC and CAQ?

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \angle \mathrm{PAB}=70 \mathrm{and} \angle \mathrm{ACS}=100 \\ \mathbf{\angle }\mathbf{PAB}\mathbf{=}\mathbf{\angle }\mathbf{ABC}\mathbf{=}\mathbf{70}\mathbf{ }\left(\mathbf{Alternate}\mathbf{ }\mathbf{angles}\right) \\ \mathrm{As} \mathrm{Exterior} \mathrm{angle}=\mathrm{Sum} \mathrm{of} \mathrm{two} \mathrm{opposite} \mathrm{interior} \mathrm{angles} \\ \Rightarrow 100=\angle \mathrm{ABC}+\angle \mathrm{BAC} \\ \Rightarrow 100=70+\angle \mathrm{BAC} \\ \mathbf{\Rightarrow }\mathbf{\angle }\mathbf{BAC}\mathbf{=}\mathbf{30} \\ \mathrm{By} \mathrm{linear} \mathrm{pair} \mathrm{axiom}, \mathrm{we} \mathrm{have}, \\ \angle \mathrm{PAB}+\angle \mathrm{BAC}+\angle \mathrm{CAQ}=180 \\ \Rightarrow 70+30+\angle \mathrm{CAQ}=180 \\ \Rightarrow 100+\angle \mathrm{CAQ}=180 \\ \mathbf{\Rightarrow }\mathbf{\angle }\mathbf{CAQ}\mathbf{=}\mathbf{80} \end{gathered}$$

Hope this information will clear your doubts about this topic.

If you have any doubts just ask here on the ask and answer forum and our experts will try to help you out as soon as possible.
Regards