Question

ABCD is a quadrilateral in which AB||DC and AD||BC.find angle b,c,d and angle a=50°

Answer 1

Since two pairs of opposite sides are equal (as given AB ║ DC and AD ║ BC)
⇒ the given quadrilateral is a parallelogram 
Since opposite angles of a parallelogram are equal 
⇒ ∠a = ∠c = 50°
similarly ∠d = ∠b , let it be equal to x .
Then the sum of all the angles of a quadrilateral is equal to 360°
⇒ ∠a + ∠b + ∠c + ∠d = 360° 
⇒ 50° + x + 50° + x = 360 °
⇒ 100° + 2x = 360 °
⇒ 2x = 360 - 100
⇒ 2x = 260 
⇒ x = 130°
⇒ ∠ b = ∠d = 130°

Answer 2

a quadrilateral with opposite sides equal is a parallelogram.
so a=c and b=d
    and a+b+c+d=360
∴a=c=50 and b=d=180-50=130