Answer:
[tex]\text{B. }80^\circ[/tex]
Step-by-step explanation:
[tex]\text{Solution:}[/tex]
[tex]1.\ \text{reflex }\text{m}\angle\text{E}=260^\circ\ \ \ [\text{Central angle is equal to the corresponding arc}[/tex]
[tex]\text{measure.]}[/tex]
[tex]\text{2. m}\angle\text{E}=360^\circ-\text{reflex }\text{m}\angle\text{E}=360^\circ-260^\circ=100^\circ[/tex]
[tex]\text{3. ED}\perp\text{AD and EB}\perp\text{AB}\ \ \ [\text{Radius is perpendicular to tangent at the point }[/tex]
[tex]\text{of contact.]}[/tex]
[tex]\text{4. m}\angle\text{EDA}=\text{m}\angle\text{EBA}=90^\circ\ \ \ \text{[From statement 2.]}[/tex]
[tex]\text{5. m}\angle\text{A}+\text{m}\angle\text{EDA}+\text{m}\angle\text{EBA}+\text{m}\angle\text{E}=360^\circ\ \ \ [\text{Sum of angles of quadrilateral}[/tex]
[tex]\text{is 360}^\circ.][/tex]
[tex]\text{or, m}\angle\text{A}+90^\circ+90^\circ+100^\circ=360^\circ\\\\\text{or, m}\angle\text{A}+280^\circ=360^\circ\\\\\text{or, m}\angle\text{A}=80^\circ[/tex]