x = 109° and y = 4.
**Step 1: Use corresponding angles to find angle relationships.**
Since quadrilaterals ABCD and FGCD are congruent, corresponding angles must be equal. Therefore:
Angle B = Angle F (congruent bases)
Angle C = Angle G (congruent bases)
**Step 2: Apply angle sum theorem to find missing angles.**
In quadrilateral ABCD, the sum of all angles is 360 degrees.
We know <A = 91° and <D = 94°.
Therefore, <B + <C = 360° - <A - <D = 360° - 91° - 94° = 75°.
**Step 3: Substitute information to solve for x and y.**
We know from step 1 that <B = <F.
We are also given that <F = 4x + 21°.
Therefore, <B = 4x + 21°.
Similarly, we know <C = <G.
We are given that BA = 3y + 2 and GF = 14.
Since AB and FG are corresponding sides in congruent quadrilaterals, they must be equal.
Therefore, 3y + 2 = 14.
Solving for y, we get y = 4.
**Step 4: Solve for x using the value of y.**
We know that <B = 4x + 21°.
We also know from step 2 that <B contributes to the sum of 75° with <C.
Since we found y = 4, we can calculate <C using the angle sum theorem for triangle BCG. We know <G = 94° and <B = 4x + 21°.
Therefore, <C = 180° - <B - <G = 180° - (4x + 21°) - 94° = 65° - 4x.
Substituting for <B and <C in the sum of angles for quadrilateral ABCD, we get: <A> + <B> + <C> + <D> = 360°
91° + (4x + 21°) + (65° - 4x) + 94° = 360°
Simplifying the equation, we get 251° - 0x = 360°
Solving for x, we get x = 109°.
Therefore, the values of x and y are:**
* x = 109°
* y = 4