Question

I need to find the value of x

Answer 1

Since the two angles are supplementary, you can set them equal to 180 degrees:
(7x-1)+(6x-1)=180
add like terms:
13x-2=180
add 2 to both sides of the equation to have the term with x alone on one side of the equation:
13x=182
divide both sides by 13 to get the value of x:
x=14

Answer 2

Hello, 

We know that all the angles shown add up to 360 (think of a circle).

We also know that the angle of (6x-1)° is congruent to the angle opposite of it. (the "top left" angle) = 6x - 1°

We also know that the angle of (7x-1)° is congruent to the angle opposite of it. 
(the "bottom left" angle) = 7x -1°

Knowing the sum of all angles as well as the angle measures in terms of x, we can add all the angle measures and equal it to 360.

So, we get (7x - 1) + (7x - 1) + (6x - 1) + (6x - 1) = 360
Simplify and we get:
26x - 4 = 360
Add 4 to both sides to get 26x = 364 
Divide by 26 on both sides to get 14.

x = 14

Hope this helps!