Mathematics

The measure of $$q$$ in the  given figure is :


ANSWER

$$152^{\circ}$$


SOLUTION
From the figure
$$\angle AOC=\angle AOB+\angle BOC$$
$$\Rightarrow \angle ADC={ 62 }^{ \circ  }+{ 90 }^{ \circ  }\\ \Rightarrow \angle ADC={ 152 }^{ \circ  }$$
Now $$\angle DOE=\angle AOC$$  (Vertically opposite angles)
$$\Rightarrow q=152^{\circ}$$
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