Question

In Fig. 16.185, if ABC is an equilateral triangle. Find ∠BDC and ∠BEC

Answer 1

∠BDC = 60°   , ∠BEC = 120°

Step-by-step explanation:

ABC is an equilateral triangle

=> ∠A = ∠BAC = 60°    ( Angles of equilateral triangle = 60°)

∠BDC = ∠BAC   ( Angle formed by same chord BC in same arc segment)

=> ∠BDC = 60°  

ABEC is a concylci quadrilateral  as all points lies on a circle

∠BAC + ∠BEC = 180°  ( Sum of oppoiste angle of Concylcic quadrilateral = 180°)

=> 60° + ∠BEC = 180°

=> ∠BEC = 120°

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

ABC is an equilateral triangle

=> ∠A = ∠BAC = 60° ( Angles of equilateral triangle = 60°)

∠BDC = ∠BAC ( Angle formed by same chord BC in same arc segment)

=> ∠BDC = 60°

ABEC is a concylci quadrilateral as all points lies on a circle

∠BAC + ∠BEC = 180° ( Sum of oppoiste angle of Concylcic quadrilateral = 180°)

=> 60° + ∠BEC = 180°

=> ∠BEC = 120°