Question 1167444
i believe you are talking about alternate interior angles formed by two lines intersected by a transversal.


if the two lines are parallel, then the alternate interior angles are congruent, i.e. equal.


angle 6 and 7 are alternate interior angles of parallel lines.


therefore, they are equal.


you get:


30x + 30 = 45x - 30
subtract 30x from both sides of the equation and add 30 to both sides of the equation to get:
60 = 15x
solve for x to get:
x = 60/15 = 4


angle 6 is equal to 30x + 30 = 120 + 30 = 150
angle 7 is equal to 45x - 30 = 180 - 30 = 150


both angles are equal, so the value of each angle is good.


angle 6 and angle 7 are each equal to 150 degrees.


here's a reference.


<a href = "https://www.storyofmathematics.com/alternate-interior-angles#:~:text=Alternate%20interior%20angles%20are%20angles,opposite%20sides%20of%20the%20transversal." target = "_blank">https://www.storyofmathematics.com/alternate-interior-angles#:~:text=Alternate%20interior%20angles%20are%20angles,opposite%20sides%20of%20the%20transversal.</a>