Construct a heptagon and show its exterior angles. Write true or false for the following statements regarding exterior angles: a) For a triangle, there are 6 exterior angles. b) For a convex polygon,

Hey Wendimuu, good to see you again. Here are the solutions to the exercises: Exercise 6.5 1. Construct a heptagon and show its exterior angles. A heptagon is a polygon with 7 sides. To construct a regular heptagon: Draw a circle. Divide the circle into 7 equal sectors. The angle for each sector at the center would be (360^)/(7) ≈ 51.43^. Connect the points where the sector lines intersect the circle to form the 7 sides of the heptagon. To show the exterior angles*, extend each side of the heptagon outwards. The angle formed between the extended side and the adjacent side of the polygon is an exterior angle. There will be 7 exterior angles, one at each vertex. 2. Write true or false for each statement. a)* For a triangle, there are 6 exterior angles. A triangle has 3 vertices. At each vertex, there is one distinct exterior angle (formed by extending one side). While you can draw two lines extending from a vertex, the two exterior angles formed are vertically opposite and thus equal. Therefore, a triangle has 3 exterior angles. Answer: False b)* For convex polygon, each exterior angle is less than 180^. In a convex polygon, all interior angles are less than 180^. Since an interior angle and its corresponding exterior angle sum to 180^, if the interior angle is less than 180^, the exterior angle must also be less than 180^ (and greater than 0^). Answer: True c)* Each exterior angle of a rectangle is 90^. A rectangle has four interior angles, each measuring 90^. The exterior angle is found by subtracting the interior angle from 180^. 180^ - 90^ = 90^ Answer: True d)* If the measure of each interior angle of a regular polygon is x^, then the measure of each exterior angle of the given regular polygon is (360 - x)^. The sum of an interior angle and its corresponding exterior angle is always 180^. If the interior angle is x^, then the exterior angle is 180^ - x^. Answer: False Sum of the exterior angles of a polygon What can you say about the sum of exterior angles of a polygon? The sum of the exterior angles of any convex polygon is always 360^. Does the sum depend on the number of sides of the polygon? No, the sum of the exterior angles of a convex polygon does not depend on the number of sides. It is always 360^, whether it's a triangle (3 sides), a quadrilateral (4 sides), or a heptagon (7 sides). Send me the next one 📸