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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.

(2x + 16) + (x) = 180

step-by-step explanation:

given,

abcd is a quadrilateral inscribed in a circle

angle a is labeled x plus 16, (x + 16)

angle b is labeled x degrees, (x)

angle c is labeled 6x minus 4, (6x – 4)

angle d is labeled 2x plus 16, (2x + 16)

what equation can be used to solve for angle b?

we know that the sum of the opposite angles of a simple quadrilateral inscribed in a circle is 180 degrees.

angle b is opposite angle d

therefore, angle b + angle d = 180

(x) + (2x + 16) = 180 

same as (2x + 16) + (x) = 180