6.1.1 Understand and use angle properties (3)
This week's tasks continue the angle chasing theme, and where again it might help to add auxiliary lines or to transform part of the given figure, for example by a translation or rotation. However, the context no longer involves regular polygons.
The task can be solved in a rich variety of ways. Here are some of the methods that were posted on Twitter:
The above methods all involve auxiliary lines. It is also possible to solve the task using transformations, for example a rotation, as here, where the parallel lines become orthogonal:
Here is an elegant, and perhaps the most common, way of solving the task:
As in the previous task, the size of a is the sum of the two given angles: