Question

ABCD is a cyclic quadrilateral whose diagonals intersect at P. If ∠DBC = 72° and ∠BAC = 42°, then the measure of ∠BCD (in degrees) is:
1. 66
2. 60
3. 65
4. 57

Answer 1

Correct Answer - Option 1 : 66

Given:

∠DBC = 72° 

∠BAC = 42° 

Calculation:

For chord CD,

∠CBD = ∠CAD ....(Angles in same segment)

∠CAD = 72° 

∠BAD = ∠BAC + ∠CAD = (42° + 72°)

⇒ 114° 

 ∠BCD + ∠BAD 180° ..(opposite angles of a cyclic quadrilateral)

⇒ ∠BCD + 114° = 180° 

⇒ ∠BCD = (180° – 114°)

⇒ ∠BCD = 66° 

∴ The required angle of ∠BCD is 66°