Angle A is circumscribed about circle O. What is the measure of angle O? [picture below]

Question

asked Aug 25, 2022 145k views

1 Answer

Vana · Answer 1 · 2022-08-30T21:09:15+0000

Answer:

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)

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

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

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

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

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

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

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