Correct Answer - Option 1 : 35°
Given:
Points A, B and C lie on the circumference of circle and form ΔABC.
BC is the diameter of circle with center O.
∠ABC = 55°
Concepts used:
Sum of all three angles of triangle is 180°.
According to Thales theorem, the angle formed by the diameter of circle at the point on circle is equal to 90°.
Calculation:
A lies on circumference of circle and lies opposite to diameter BC of circle of centre O.
Applying Thales theorem in ΔABC,
⇒ ∠BAC = 90°
Sum of all three angles of triangle is 180°.
⇒ ∠BAC + ∠ABC + ∠ACB = 180°
⇒ 90° + 55° + ∠ACB = 180°
⇒ ∠ACB = 180° - 145°
⇒ ∠ACB = 35°
∴ Measure of ∠ACB is 35°.