a) 108°
Answer:
b) 54°
Step-by-step explanation:
a) By arc sum property of a circle.
[tex] m\widehat {AEB} + m\widehat {AB} = 360°\\
252° + m\widehat {AB} = 360°\\
m\widehat {AB} = 360°- 252°\\
\huge \red {\boxed {m\widehat {AB} = 108°}} \\[/tex]
b) In the given figure, DC is tangent to the circle with O at point A and AB is chord or secant. Therefore, by tangent secant theorem:
[tex] m\angle BAC = \frac{1}{2} \times m\widehat {AB}\\\\
\therefore m\angle BAC = \frac{1}{2} \times 108°\\\\
\huge \purple {\boxed {m\angle BAC = 54°}} [/tex]
