Question

1. what is the value of x?

(4x + 5)°
(8x - 6)°

Explanation:

Step1: Identify angle relationship

The figure is a parallelogram (marked congruent sides), so consecutive angles are supplementary. Also, the angle $(4x+5)^\circ$ is equal to the adjacent angle inside the parallelogram, and this angle plus $(8x-6)^\circ$ equals $180^\circ$.

Step2: Set up the equation

$$(4x + 5) + (8x - 6) = 180$$

Step3: Simplify the left side

Combine like terms:
$$12x - 1 = 180$$

Step4: Solve for $x$

Add 1 to both sides, then divide by 12:
$$12x = 181$$
$$x = \frac{181}{12} \approx 15.08$$

Answer:

$x = \frac{181}{12}$ or approximately $15.08$