Question

How can I solve this problem?

Answer 1

a) 108°

Answer:

b) 54°

Step-by-step explanation:

a) By arc sum property of a circle.

$m\widehat {AEB} + m\widehat {AB} = 360°\\252° + m\widehat {AB} = 360°\\m\widehat {AB} = 360°- 252°\\\huge \red {\boxed {m\widehat {AB} = 108°}}$

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:

$m\angle BAC = \frac{1}{2} \times m\widehat {AB}\\\\\therefore m\angle BAC = \frac{1}{2} \times 108°\\\\\huge \purple {\boxed {m\angle BAC = 54°}}$