g = 40°, f = 50°
Step-by-step explanation:
Step 1: If two tangents are drawn to a circle from one external point, then the tangents are equal in length.
So, ΔABC is an isosceles triangle.
⇒∠BAC = ∠ACB – – – – (1)
Step 2: Sum of the interior angles of the triangle is 180°.
In ΔABC, ∠BAC + ∠ACB + ∠CBA = 180°
⇒∠BAC + ∠BAC + 80° = 180° (using(1))
⇒2∠BAC = 180° – 80° = 100°
⇒∠BAC = 50°
⇒∠ACB = f = 50°
Step 3: Tangent of the circle is always perpendicular to the radius.
∠OAC + ∠BAC = 90°
∠OAC + 50° = 90°
∠OAC = 40°
∠OAC = g = 40°
Hence, f = 50° and g = 40°.
