The value of x is 18 and the value of ∠A (interior angle) is 73°.
According to the given figure,
We have:
∠A = 6x-35°
∠B = 3x+53°
The two parallel lines have been cut by another line.
(Note that when a line divides two parallel lines then the sum of the interior angles on the same side is 180° and the alternate interior angles are equal to each other.)
So, we will have the following expression:
∠A + ∠B = 180°
(6x-35+3x+53)° = 180°
9x+18 = 180
9x = 180-18
9x = 162
x = 162/9
x = 18
Now, putting the value of x in ∠A,
∠A = 6x-35°
∠A = (6*18-35)°
∠A = (108-35)°
∠A = 73°
Hence, the value of x is 18 and the measurement of ∠A is 73°.
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