Question

In the given figure , triangle ABC and triangle DBC are inscribed in a circle such that angle BAC =60° and angle DBC =50° then angle BCD =

a) 50°
b) 70°
c) 60°
d)80°​

Answer 1

Answer :- angle BCD = 60°

STEP BY STEP EXPLAINS:-

angle BAC = angle BCD (Segment of the same circle are equal)

∆BDC:-

BDC+ BCD+ DBC = 180°

60° + BCD+ 50° = 180°

BCD = 70° ans

Answer 2

Given:

• ∠BAC = 60°
• ∠DBC = 50°

To Find:

• ∠BCD

Solution:

• From the figure given, we can come to few conclusions,
• ∠BAC = ∠BDC = 60° (∵ Angles in the same segment of circles are the same).
• Considering ΔBDC,
• We know the rule, Sum of all three angles of triangle = 180°
• So, ∠BDC+∠DBC+∠BCD = 180°
• Substituting the values we get,
• 60°+50°+∠BCD = 180°
• ∠BCD = 180°-110° =  70°

The angle of BCD, ∠BCD = 70°.