@divinedolphin The short answer is that the purple angle \(\angle a\) has measure \(\angle a\) because the other purple angle in the purple triangle has measure \(90^{\circ} - a,\) since the angles of a triangle add up to \(180^{\circ}.\)

M2W2D5-ch-part-5-purple-angles-complementary.png

Then, why is the other purple angle equal to \(90^{\circ} - a?\)

Well, this is because if you start at the yellow angle that is \(\angle a\) and then look at the purple angle that right next to the box corner that is adjacent to it, you can see that these three angles together make up a line:

M2W2D5-ch-part-5-yellow-and-purple-complementary.png

This is because a line has \(180^{\circ}\) degrees, and the right corner accounts for \(90^{\circ}\) of these degrees.

I hope this helps! 🙂

Hi Xiao Ma,

Given what we know about trapezoids (namely that one pair of sides is perpendicular), it doesn't matter if the left and right sides aren't parallel. We just need to know that the top and bottom are parallel.

Happy Learning,

The Daily Challenge Team