Let's draw the figures to better understand the scenario:
The figure appears that ∠A and ∠E are pairs of corresponding angles. Since it was given that the two quadrilaterals are congruent, ∠A and ∠E must also be congruent.
With this relationship, let's first determine the value of x to be able to determine the measure of ∠A.
We get,
[tex]\text{ 6x - 8 = 4x + 1}[/tex][tex]\text{ 6x - 8 + 8 - 4x = 4x + 1 + 8 - 4x}[/tex][tex]\text{ 6x - 4x = 1 + 8}[/tex][tex]\text{ 2x = 9}[/tex][tex]\text{ }\frac{\text{2x}}{2}\text{ = }\frac{\text{9}}{2}[/tex][tex]\text{ x = }\frac{9}{2}[/tex]
Let's determine the measure of ∠A.
[tex]\text{ }\angle A\text{ = 6x - 8 = 6(}\frac{9}{2})\text{ - 8}[/tex][tex]\text{ = 3(9) - 8}[/tex][tex]\text{ = 27 - 8}[/tex][tex]\text{ }\angle A=19^{\circ}[/tex]
Therefore, the measure of ∠A is 19°. The answer is letter A or the 1st option.
