Hi! Can you please explain number 1 on page 242 on the 4th edition of the PWN book?

The trick here is to extend one of the segments to create a transversal (and a triangle). Then it’s all about just adding up to 180°.

Extending a segment and filling in all the 128° angles we know:

And then of course we can fill in some 52° angles because .

Now what about that 59° angle. What’s its supplement? That’s right, 121°.

Now you have a triangle with two known angles: 121° and 52°. What’s the last angle? Right, just 7°!