Question

Angle A is circumscribed about circle O.

What is the measure of angle O?

[picture below]

Answer 1

134°

Explanation:

`In\: \odot O,` AB and AC are tangents at points B and C respectively. OB and OC are radii.

`\therefore OB\perp AB\: \&\: OC\perp AC`

(By tangent radius theorem)

`\therefore m\angle ABO =m\angle ACO = 90\degree`

`m\angle CAB+ m\angle ABO +m\angle ACO+ m\angle BOC = 360\degree`

`\therefore 46\degree + 90\degree +90\degree+ m\angle BOC = 360\degree`

`\therefore 226\degree + m\angle BOC = 360\degree`

`\therefore m\angle BOC = 360\degree-226\degree`

`\therefore m\angle BOC = 134\degree`

`\implies m\angle O= 134\degree`