Middle School

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------------------------------------------------ please help

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AOD is 62 degrees btw

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Answer :

Step-by-step explanation:

a)

DA is tangent and at point A and OA is radius of the circle.

[tex] \therefore OA \perp DA\\

\therefore \angle OAD = 90°\\

In\: \triangle AOD\\

m\angle AOD= 180° - (m\angle OAD + m\angle ODA) \\

\therefore m\angle AOD= 180° -(90°+28°)\\

\therefore m\angle AOD= 180° -118°\\

\huge \red {\boxed {\therefore m\angle AOD=62°}} \\\\

b) \\

\because m\angle ABC = \frac{1}{2} \times m\angle AOD\\[/tex]

(Angle formed at the circumference of the circle is half the angle formed at the center of the circle)

[tex] \therefore m\angle ABC = \frac{1}{2} \times 62°\\

\huge \red {\boxed {\therefore m\angle ABC = 31°}}[/tex]