The problem requires us to complete a table relating angles to their complements and supplements. Recall that two angles are complementary if their sum is $90^{\circ}$, and two angles are supplementary if their sum is $180^{\circ}$. If an angle's complement or supplement does not exist (i.e., requires a negative angle), we write "N/A".

1. Problem Description

The problem requires us to complete a table relating angles to their complements and supplements. Recall that two angles are complementary if their sum is $90^{\circ}$, and two angles are supplementary if their sum is $180^{\circ}$. If an angle's complement or supplement does not exist (i.e., requires a negative angle), we write "N/A".

2. Solution Steps

We will fill in the table row by row.

Row 1: Angle is $53^{\circ}$.

Complement: Let the complement be $x$. Then $53 + x = 90$, so $x = 90 - 53 = 37$. The complement is $37^{\circ}$.

Supplement: Let the supplement be $y$. Then $53 + y = 180$, so $y = 180 - 53 = 127$. The supplement is $127^{\circ}$.

Row 2: Supplement is $121^{\circ}$.

Angle: Let the angle be $z$. Then $z + 121 = 180$, so $z = 180 - 121 = 59$. The angle is $59^{\circ}$.

Complement: Let the complement be $w$. Then $59 + w = 90$, so $w = 90 - 59 = 31$. The complement is $31^{\circ}$.

Row 3: Complement is $28^{\circ}$.

Angle: Let the angle be $a$. Then $a + 28 = 90$, so $a = 90 - 28 = 62$. The angle is $62^{\circ}$.

Supplement: Let the supplement be $b$. Then $62 + b = 180$, so $b = 180 - 62 = 118$. The supplement is $118^{\circ}$.

Row 4: Supplement is $67^{\circ}$.

Angle: Let the angle be $c$. Then $c + 67 = 180$, so $c = 180 - 67 = 113$. The angle is $113^{\circ}$.

Complement: Let the complement be $d$. Then $113 + d = 90$, so $d = 90 - 113 = -23$. Since the complement is negative, it does not exist. We write "N/A".

Row 5: Angle is $234^{\circ}$.

Complement: Let the complement be $e$. Then $234 + e = 90$, so $e = 90 - 234 = -144$. Since the complement is negative, it does not exist. We write "N/A".

Supplement: Let the supplement be $f$. Then $234 + f = 180$, so $f = 180 - 234 = -54$. Since the supplement is negative, it does not exist. We write "N/A".

3. Final Answer

Here is the completed table:

Angle | Complement to angle | Supplement to angle

------- | -------- | --------

$53^{\circ}$ | $37^{\circ}$ | $127^{\circ}$

$59^{\circ}$ | $31^{\circ}$ | $121^{\circ}$

$62^{\circ}$ | $28^{\circ}$ | $118^{\circ}$

$113^{\circ}$ | N/A | $67^{\circ}$

$234^{\circ}$ | N/A | N/A