**M5+**

This again involves a rotation, this time through 90˚.

The original two green lines now form a single straight line (actually, ‘line segment’).

So we have formed a triangle with angles u and v; the third angle is 90˚ because one of the red lines (which was parallel to the other red line), has turned through 90˚.

Thus u + v +90˚ = 180˚, so v = 90˚ – u.

The original two green lines now form a single straight line (actually, ‘line segment’).

So we have formed a triangle with angles u and v; the third angle is 90˚ because one of the red lines (which was parallel to the other red line), has turned through 90˚.

Thus u + v +90˚ = 180˚, so v = 90˚ – u.

This is rather neat, but if we see geometry as a logically ordered system it can also be regarded as rather convoluted compared to Method 1, say. This is because we use parallel line properties to prove the angle sum of a triangle.