Students will be given an introduction to radians. A demonstration can be seen by watching this, then this, and finally, this. Then students will learn how to determine the quadrant in which an angle lies, whether it be expressed in degrees or radians. Finally, students will learn how to sketch angles in radians.

Concude by giving your students this challenge:

Find \(x{:}\)

There are two elegant ways to solve this problem, both of which can be done mentally. Here's the first way: Notice that \(ACEDB\) is a pentagon, and thus, it's interior angles sum to \(540^\circ.\) Notice that \(\angle DEC = 360^\circ - 160^\circ = 200^\circ.\) Adding up the known angles in the pentagon, gives us \(80^\circ + 20^\circ + 200^\circ + 10^\circ = 310^\circ.\) But we need \(540^\circ,\) so the missing angle, \(\angle BDE,\) must be \(230^\circ.\) Thus, \(x = 360^\circ - 230^\circ = 130^\circ.\) Here's the second way: Start by drawing \(\overline{BC}.\) Notice that \(\triangle ABC\) has \(80^\circ + 20^\circ + 10^\circ = 110^\circ,\) so it's lacking \(70^\circ.\) Also, notice that \(BDEC\) is a quadrilateral, and thus, it's interior angles sum to \(360^\circ.\) Adding up the known angles in the quadrilateral, gives us \(160^\circ + 70^\circ = 230^\circ,\) but we need \(360^\circ,\) so \(x = 360^\circ - 230^\circ = 130^\circ.\)

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