Question

How can I solve this problem?

Answer 1

a) 108°

Answer:

b) 54°

Explanation:

a) By arc sum property of a circle.

`m\widehat {AEB} + m\widehat {AB} = 360°\\</p><p>252° + m\widehat {AB} = 360°\\</p><p>m\widehat {AB} = 360°- 252°\\</p><p>\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 = (1)/(2) * m\widehat {AB}\\\\</p><p>\therefore m\angle BAC = (1)/(2) * 108°\\\\</p><p>\huge \purple {\boxed {m\angle BAC = 54°}}`