Question

AC is the diameter of the circumcircle of the cyclic quadrilateral ABCD. If ∠BDC = 42°, then what is ∠ACB equal to?

(a) 42° 

(b) 45° 

(c) 48° 

(d) 58°

Answer 1

Answer: (c) 48º 

∠CAB = ∠CDB = 42° (∠s in the same segment are equal) 

∠ABC = 90° (∠ in a semicircle = 90°) 

∴ In ∆ ABC, ∠ACB = 180° – (∠CAB + ∠ABC) 

= 180° – (90° + 42°) = 48°