**M3A+**

Another doodle.

Here we have (somehow) hit upon drawing a completely new line, which again produces a triangle.

We know one of its angles is 90˚ [given] so the sum of the other two is 90˚. We don’t know their specific values but we can write them as, say, e and 90˚– e.

Thus u + e + 90˚– e + v = 180˚ [‘supplementary angles’ property],

so u + v = 90˚, so v = 90˚ – u.

Here we have (somehow) hit upon drawing a completely new line, which again produces a triangle.

We know one of its angles is 90˚ [given] so the sum of the other two is 90˚. We don’t know their specific values but we can write them as, say, e and 90˚– e.

Thus u + e + 90˚– e + v = 180˚ [‘supplementary angles’ property],

so u + v = 90˚, so v = 90˚ – u.