Question

The first one asks for the value of x. I need help on both. I am struggling to understand how to do this, please help

Answer 1

(1) since the horizontal lines are parallel, and you know the vertical intersecting line crosses at right angle, it must be that the two angles with variable x sum up to 90 degrees. So same rewritten as an equation:

x+8+6x-58 = 90

7x = 140

x = 20 (degrees)

(2) here you have two variable so you will need to find two equations.

The first one comes from the triangle and its angles summing up to 180:

63 + (3x+45) + (y-6) = 180

The second one comes from the fact that the two horizontal lines are parallel and so the angles (7x-7) and (3x+45) must be the same:

7x-7=3x+45

Let's solve the last one first:

4x = 52

x = 13

then plug this solution into the first equation and solve for y

63 + (3x+45) + (y-6) = 180

3x + y = 78

y = 78-39 = 39

so the value of y is 39 (degrees)