1. **Problem:** Find the perimeter of a kite with sides 12 and 20. 2. **Formula:** Perimeter of a kite = 2 × (sum of lengths of two distinct adjacent sides). 3. **Calculation:** $$\text{Perimeter} = 2 \times (12 + 20)$$ $$= 2 \times 32$$ $$= 64$$ 4. **Answer:** The perimeter is 64. 1. **Problem:** Find $x$ and $y$ in a kite with angles 180° and 29°. 2. **Rule:** The sum of interior angles in any quadrilateral is 360°. 3. **Calculation:** $$180 + 29 + x + y = 360$$ $$x + y = 360 - 209 = 151$$ 4. **Answer:** $x + y = 151$ (cannot solve uniquely without more info). 1. **Problem:** Find $x$ and $y$ in an isosceles trapezoid with angle 128° and variables $x$, $y$. 2. **Rule:** Consecutive angles between parallel sides are supplementary. 3. **Calculation:** $$128 + y = 180 \Rightarrow y = 52$$ $$x = y = 52$$ (isosceles trapezoid has equal base angles) 4. **Answer:** $x = 52$, $y = 52$. 1. **Problem:** Kite perimeter = 86 ft, sides are $3y$, $5x - 15$, $2x + 3$, $6y - 2$. 2. **Rule:** Kite has two pairs of equal adjacent sides. 3. **Equations:** $$3y = 5x - 15$$ $$2x + 3 = 6y - 2$$ 4. **Perimeter:** $$86 = 2(3y + 2x + 3)$$ $$43 = 3y + 2x + 3$$ $$40 = 3y + 2x$$ 5. **Substitute $3y = 5x - 15$:** $$40 = (5x - 15) + 2x = 7x - 15$$ $$7x = 55$$ $$x = \frac{55}{7}$$ 6. **Find $y$:** $$3y = 5 \times \frac{55}{7} - 15 = \frac{275}{7} - 15 = \frac{275 - 105}{7} = \frac{170}{7}$$ $$y = \frac{170}{21}$$ 7. **Answer:** $$x = \frac{55}{7} \approx 7.86, \quad y = \frac{170}{21} \approx 8.10$$ 1. **Problem:** Isosceles trapezoid perimeter = 164 cm, sides $y+12$, $7x$, $y-12$, $81$, $y$. 2. **Rule:** Perimeter is sum of all sides. 3. **Equation:** $$164 = (y+12) + 7x + (y-12) + 81 + y$$ $$164 = 3y + 7x + 81$$ $$83 = 3y + 7x$$ 4. **Answer:** Cannot solve uniquely without more info. 1. **Problem:** Isosceles trapezoid perimeter = 85 cm, sides 18 cm, $x$, 37 cm. 2. **Rule:** Perimeter = sum of all sides. 3. **Equation:** $$85 = 18 + x + 37 + x$$ $$85 = 55 + 2x$$ $$2x = 30$$ $$x = 15$$ 4. **Answer:** $x = 15$ cm. 1. **Problem:** Kite with angles 146°, 47°, sides $x$, $y$. 2. **Rule:** Sum of angles = 360°. 3. **Equation:** $$146 + 47 + x + y = 360$$ $$x + y = 167$$ 4. **Answer:** $x + y = 167$ (cannot solve uniquely). 1. **Problem:** Trapezoid with angles 115°, $18y$, $(3x + 5)$°, $(10y)$°. 2. **Rule:** Sum of angles = 360°. 3. **Equation:** $$115 + 18y + 3x + 5 + 10y = 360$$ $$3x + 28y + 120 = 360$$ $$3x + 28y = 240$$ 4. **Answer:** Cannot solve uniquely without more info. 1. **Problem:** Kite with angles 41°, 59°, $(4x - 3)$°, $y$. 2. **Rule:** Sum of angles = 360°. 3. **Equation:** $$41 + 59 + 4x - 3 + y = 360$$ $$97 + 4x + y = 360$$ $$4x + y = 263$$ 4. **Answer:** Cannot solve uniquely. 1. **Problem:** Isosceles trapezoid perimeter = 88 ft, sides 24, $x - 4$, $3x + 2$. 2. **Rule:** Perimeter = sum of all sides. 3. **Equation:** $$88 = 24 + (x - 4) + 24 + (3x + 2)$$ $$88 = 46 + 4x - 2$$ $$88 = 44 + 4x$$ $$4x = 44$$ $$x = 11$$ 4. **Answer:** $x = 11$. 1. **Problem:** Polygon with angles 137°, 22°, sides $x$, $y$. 2. **Rule:** Sum of angles in polygon depends on number of sides (not given). 3. **Answer:** Cannot solve uniquely without more info. 1. **Problem:** Polygon with angles 78°, 41°, sides $x$, $y$. 2. **Rule:** Sum of angles depends on polygon type. 3. **Answer:** Cannot solve uniquely without more info.