Question

Line BC is tangent to the circle centered at A. Find the measure of angle BCA. Explain or show your reasoning.

Answer 1

Answer:

$m\angle BCA= 33\degree$

Step-by-step explanation:

$In\: \odot A$ BC is tangent to the circle at point B.

Therefore, by tangent-radius theorem:

$\therefore AB\perp BC$

$\therefore \angle ABC = 90\degree$

$In\: \triangle ABC,$

$m\angle ABC +m\angle BAC +m\angle BCA= 180\degree$

$90\degree+57\degree +m\angle BCA= 180\degree$

$147\degree +m\angle BCA= 180\degree$

$m\angle BCA= 180\degree - 147\degree$

$m\angle BCA= 33\degree$