Question

in the given figure determine a,b,c

Answer 1

a=90°
b=28°
c=62°
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Answer 2

Consider the cyclic quadrilateral AEDB,
∠BAE + ∠BDE = 180°  [opposite angles of a cyclic quadrilateral are supplementary]
⇒ 62° + ∠BDE = 180°
⇒ ∠BDE = 180° - 62° = 118°
Again, ∠BDE + ∠BDC = 180°  [Linear pair angles]
⇒ 118° + ∠BDC = 180°
⇒ ∠BDC = 62°
⇒ ∠a =  ∠BDC + ∠BCD  [The exterior angle of a triangle is equal to sum of two interior opposite angles]
⇒ ∠a =  62° + 43° = 105°
Again, ∠a + ∠AED = 180°  [As opposite angles of a cyclic quadrilateral are supplementary]
⇒ 105° + ∠AED = 180°
⇒ ∠AED = 75°
Now, in triangle DEF,
∠AED =  ∠c + ∠b  [Again, the exterior angle of a triangle is equal to sum of two interior opposite angles]
⇒  ∠c + ∠b = 75°
Now, the value of  ∠c and ∠b can't be found from above equation based on the information provided by you.
Please recheck your query.