Answer:
m(∠OAC) = 52°
Step-by-step explanation:
A, B and C are the pints on a circle with center O.
m(∠ABC) = 38°
By the central angle theorem,
"Central angle subtended by two points on a circle measure the twice of the inscribed angle subtended by these points."
m(∠AOC) = 2m(∠ABC)
m(∠AOC) = 2 × 38° = 76°
Now in ΔAOC,
AO and OC are the radii, so the angles opposite to radii will measure the same.
∠OAC ≅ ∠OCA
Since, sum of all the interior angles of a triangle is 180°.
m(∠OAC) + m(∠OCA) + m(∠AOC) = 180°
m(∠OAC) + m(∠OAC) + 76° = 180°
2m(∠OAC) = 180° - 76°
2m(∠OAC) = 104°
m(∠OAC) = 52°
