Answer:
a) x = 45°
b) AD is parallel to BC.
Step-by-step explanation:
Here, the given angles in the quadrilateral ABCD are:
∠A = ( 2 x)° , ∠B = ( 90)° , ∠C = ( x)° and ∠D = ( 3x)°
Now, in a quadrilateral: SUM OF ALL INTERIOR ANGLES IS 360°.
⇒∠A+ ∠B+ ∠C +∠D = (180)°
or, ( 2 x)+ ( 90)° + ( x)° + ( 3x)° = (180)°
or, 6 x = 180 - 90 = 270°
or, x = 270/6 = 45°
or, x = 45°
Now, ∠A = ( 2 x)° = 2 x (45°) = 90°
⇒∠A = ∠B = 90°
So, AD and BC are two lines perpendicular to AB.
⇒ AD II BC (as two liner PERPENDICULAR to the same given lines are PARALLEL to each other)
Hence, AD is parallel to BC.
