Question

Given: circle k(O), mAB =(6x−50)°, m∠BCA=(2x)°

Find: m∠BAC

Answer 1

40°

Explanation:

arc AB has twice the measure of the inscribed angle BCA that intercepts it, so we have the relation ...

(6x-50)° = 2(2x)°

2x -50 = 0

2x = 50

So, angle BCA has measure 50°. Since AC is a diameter, angles BCA and BAC are complementary. Thus ...

m∠BAC = 90° - m∠BCA = 90° - 50°

m∠BAC = 40°