Answer:
y = 32°
Step-by-step explanation:
The central angle is twice the angle on the circle subtended by the same arc
∠ BOC = 2 × ∠ BAC , that is
x + 62 = 2(2x - 50) ← distribute
x + 62 = 4x - 100 ( subtract x from both sides )
62 = 3x - 100 ( add 100 to both sides )
162 = 3x ( divide both sides by 3 )
54 = x
Then
∠ BOC = x + 62 = 54 + 62 = 116°
Δ BOC is isosceles ( OB = OC ) so the 2 base angles are congruent
y = [tex]\frac{180-116}{2}[/tex] = [tex]\frac{64}{2}[/tex] = 32°
