In the diagram, Find the value of w

-13

Step-by-step explanation:

the angle of ACD is 180-72 = 108 degrees.

simply because every side of a line represents 180 degrees of turning potential (to flip something around on a flat ground is a 180 degree turn). and we know 72 degrees are already "taken" at the other side of the angle.

BC bisects the angle. that means it divided the angle into 2 equal parts.

so the angle between BC and k is 108/2 = 54 degrees.

because j is parallel to k, this angle is the same as the angle between BC and j.

so,

54 = 2w + 80

-26 = 2w

w = -13

d, x=8

step-by-step explanation:

simplifying

4x + -5 = 2x + 11

reorder the terms:

-5 + 4x = 2x + 11

reorder the terms:

-5 + 4x = 11 + 2x

solving

-5 + 4x = 11 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-5 + 4x + -2x = 11 + 2x + -2x

combine like terms: 4x + -2x = 2x

-5 + 2x = 11 + 2x + -2x

combine like terms: 2x + -2x = 0

-5 + 2x = 11 + 0

-5 + 2x = 11

add '5' to each side of the equation.

-5 + 5 + 2x = 11 + 5

combine like terms: -5 + 5 = 0

0 + 2x = 11 + 5

2x = 11 + 5

combine like terms: 11 + 5 = 16

2x = 16

divide each side by '2'.