Question

ABCD is a cyclic quadrilateral. If A=(2x=14) B=(5y+5) C=(4x+4) and D=50 degree. Find x.

Answer 1

A+C=180
2x+14+4x+4=180
6x+18=180
6(x+3)=180
x+3=180/6
x+3=30
x=27

Answer 2

in a cyclic quad. sum of opp. sides are supplementary

⇒∠A + ∠C = 180° and  ∠B + ∠D = 180°

so, 
    ∠B + ∠D = 180
     ⇒5y+5° +50° = 180°
     ⇒5y = 125°.
     ⇒ y = 25°

   ∠A + ∠C = 180°                          
    ⇒2x + 14° + 4x + 4° = 180°       
    ⇒ 6x + 18° = 180°                     
    ⇒ 6x = 162°                              
    ⇒ x = 27°