Answer:
1. (n-2)180
2. 360°
3. 102°
Step-by-step explanation:
In any polygon, the number of triangles than can be created by drawing lines from one vertex to every other vertex will be 2 less than the number of sides. In an octagon, 6 triangles are created. This is represented in the given equation as n-2. Since the sum of interior angles of a triangle is 180°, We know that the sum of an octagon's interior angles will be 180*6, or 1080°.
In other words, n is 2 less than the number of sides, but also the number of triangles created inside the polygon. Then we multiplied (n-2) by 180 because each triangle has interior angle sum of 180°, and we want the interior angles of all the triangles found in each polygon. That's why we use the equation (n-2)180 to find the sum of the interior angles of polygons.
The sum of exterior angles is always 360 because after going around the polygon on it's edges, we always end up in the initial direction. This is because we've turned around a whole 360°. This will happen with all polygons, so the sum of exterior angles of a polygon will always be 360°.
A parallelogram's opposite angles will always be congruent, so m∠DAB=102°
