Answer:
A is equal to 30°
Explanation:
To find the measurement of angle A, all we need to do is find the other two inner angles, which we can do with basic logic, then solve for x, and calculate a with that.
To start with because the two downward vectors intersect each other, we know that the angles on opposite sides of that intersection are identical. So the bottom angle in our triangle is equal to the outer angle on that side, 8x + 4
On the right, we know that the total of the angles between the horizontal line and the down-leftward vector must add up to 180 degrees. Because the outer angle is given as 130°, then we know that the inner must be 50°
Now with those, and the already provided angle of A, we can say:
(3x - 6) + (8x + 4) + 50 = 180
(3 + 8)x + 50 + 4 - 6 = 180
11x + 48 = 180
11x = 132
x = 12
Now with value of x found, we can easily find the value of A
A = 3x - 6
A = 3 × 12 - 6
A = 36 - 6
A = 30
So A is equal to 30 degrees.
Bonus: Now that we know A is 30 degrees, and that the upper/right angle is 50 degrees, we can say that the bottom angle is 180 - (50 + 30), or 100 degrees.