Question

crack the codeproperties of parallelogramseach of the figures pictured is a parallelogram.1. parallelogram with side lengths $7x+4$ and $3(x+8)$2. parallelogram with angles $38^\circ$, $47^\circ$, $65^\circ$, $x^\circ$3. parallelogram with angles $43^\circ$, $56^\circ$, $x^\circ$4. parallelogram with angles $(2x-6)^\circ$, $136^\circ$5. parallelogram with angles $(2x+10)^\circ$, $(3x-15)^\circ$6. parallelogram with angles $48^\circ$, $(16x)^\circ$7. parallelogram with diagonal segments $2x+2$, $5x-10$, $x-3$8. parallelogram with angles $42^\circ$, $(2x)^\circ$, $(2x+14)^\circ$9. parallelogram with angles $(3x+50)^\circ$, $(2x+30)^\circ$10. parallelogram with side lengths $8$ and $2x+4$11. parallelogram with angles $72^\circ$, $54^\circ$, $26^\circ$, $x^\circ$12. parallelogram with angles $96^\circ$, $64^\circ$, $x^\circ$

Explanation:

Step1: Solve top-right parallelogram

In a parallelogram, consecutive angles are supplementary, and the angle $x^\circ$ is supplementary to $56^\circ$.
$x = 180 - 56 = 124$

Step2: Solve middle-top parallelogram

In a parallelogram, opposite angles are equal, and vertical angles formed by diagonals are equal. First find the unknown angle in the triangle: $180 - 38 - 65 = 77$. Then $x$ is vertical to this angle, so $x = 77$.

Step3: Solve middle-left parallelogram

In a parallelogram, consecutive angles are supplementary.
$2x - 6 + 135 = 180$
$2x = 180 - 135 + 6 = 51$
$x = \frac{51}{2} = 25.5$

Step4: Solve middle-middle parallelogram

In a parallelogram, consecutive angles are supplementary.
$2x + 10 + 3x - 15 = 180$
$5x - 5 = 180$
$5x = 185$
$x = 37$

Step5: Solve middle-right parallelogram

In a parallelogram, alternate interior angles are equal.
$16x = 48$
$x = 3$

Step6: Solve bottom-middle parallelogram

In a parallelogram, consecutive angles are supplementary, and adjacent angles formed by a side extension are supplementary to the parallelogram angle.
$2x + 2x + 14 + 42 = 180$
$4x + 56 = 180$
$4x = 124$
$x = 31$

Step7: Solve bottom-right parallelogram

In a parallelogram, consecutive angles are supplementary.
$3x + 50 + 2x + 30 = 180$
$5x + 80 = 180$
$5x = 100$
$x = 20$

Step8: Solve bottom-left parallelogram

In a parallelogram, opposite sides are equal.
$2x + 4 = 8$
$2x = 4$
$x = 2$

Step9: Solve bottom-middle-left parallelogram

In a parallelogram, the sum of angles in a triangle formed by diagonals is 180.
$72 + 54 + x + 26 = 180$
$x + 152 = 180$
$x = 28$

Step10: Solve bottom-right parallelogram

In a parallelogram, vertical angles are equal, and triangle angles sum to 180. First find the unknown angle in the triangle: $180 - 96 - 64 = 20$. Then $x$ is vertical to this angle, so $x = 20$.

Answer:

Top-left: $x=5$ (already solved correctly)
Top-middle: $x=77$
Top-right: $x=124$
Middle-left: $x=25.5$
Middle-middle: $x=37$
Middle-right: $x=3$
Bottom-left (diagonals): $x=4$ (already solved correctly)
Bottom-middle-left (side): $x=2$
Bottom-middle: $x=31$
Bottom-middle-right (diagonals): $x=28$
Bottom-right: $x=20$
Bottom-right (angles): $x=20$