What is the value of d?

Step-by-step explanation:

Ok so this picture may look super super complicated but it's actually not too terrible.

The best (and only) way to start this problem is to find angle "b". To find angle "b" you can use the 107° angle next to it. When two angles are made by crossing lines the angles next to each other will always add up to 180°. so in that case:

107+b=180

b=73

Now that we know what b is we can just use our incredibly extensive knowledge of those three sided shapes I like to call triangles. If you look at the picture you can see that angles d, b(73°) and 45° make a triangles and all of them together will add up to 180° because there are 180° in a triangle. So...

d+73+45=180

d+118=180

d=62

(Disclaimer: there is another way to solve this problem but I like that way the best)

Here's the other way (i'm not going to explain this super in depth tho).

Angle a must be 45 because of the alternate angle theorem. d+a must be 107 because of the alternate angle theorem.

d+45=107

d=62