Question

in the gjven figure if triangle ABC is an equilateral triange and bd=dc find angleBCD​

Answer 1

Answer:

30°

Step-by-step explanation:

ABCD is cyclic quadrilateral ,

we know that ,

sum of opposite angles of cyclic quadrilateral is 180°,

angle BAC + angle BDC = 180°

60 + angle BDC = 180°

angle BDC = 120°

=> In ∆BDC ,

BD = DC,

angle DBC = angle BCD( angles opposite to equal sides are equal )

=> In ∆ BDC ,

By angle sum property ,

angle DBC + angle BCD + angle BDC = 180°

(as angle DBC = angle BCD)

angle BCD + angle BCD + 120 ° = 180°

2 angle BCD = 180°-120°

2 angle BCD = 60°

angle BCD = 60°/2

angle BCD = 30°