Answer

  1. 130º
    Solution:
    Construction: Through O, draw OE || AB || CD
    $\Rightarrow\angle\text{BAO}+\angle\text{EOA}=180^\circ$
    $\Rightarrow100^\circ+\angle\text{EOA}=180^\circ$
    $\Rightarrow\angle\text{EOA}=80^\circ$
    So, $\angle\text{EOC}=\angle\text{EAO}-\angle\text{COA}=80^\circ-30^\circ=50^\circ$
    Since CD || EO
    $\angle\text{OCD}+\angle\text{EOC}=1806^\circ$
    $\Rightarrow\angle\text{OCD}+50^\circ=180^\circ$
    $\Rightarrow\angle\text{OCD}=130^\circ$

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