[scheduled:: 2025-01-10]

Proving that Exterior angles of polygons add to 360

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\begin{aligned} \sum_{n} i n_{n} & = 180 (n - 2) & by dividing into triangles \\ \sum_{n} e x t_{n} & = \frac{360 n - 2 \sum_{n} i n_{n}}{2} & vertical angle pairs, supplementary angles \\ \sum_{n} e x t_{n} & = 180 n - \sum_{n} i n_{n} \\ = 180 n - 180 (n - 2) & Transitive PoE \\ = 180 n - 180 n + 360 \\ = 360 ° & QED \end{aligned}

#hw (geometry) 9.2 Angles in a Polygon (p. 246) 2025-01-15
#quiz Prove that the measure of each interior angle of a regular polygon is $\frac{180 (n - 2)}{n}$
#quiz Construct the incenter of an obtuse triangle
#quiz Construct the circumcenter of an acute triangle
#quiz Construct a line parallel to a given line, so that it passes through a given point.
#quiz Construct a line segment that is one-fifth the length of a given line segment.
#quiz Bisect a given angle
#quiz What is the formula for the sum of exterior angles for any convex polygon?
#quiz What is the formula for the measure of the interior angles for any regular polygon?