Solve for the unknown angles. Justify your answers. The local church has a triangular-shaped ornamental garden. The parish Council wants to place a statue at a point in the middle that will be an equal distance from, and perpendicular to, each of the three paths that border the garden. Describe to them how they can find this point, with a diagram to support your answer. Student Council members are designing a large poster that will tell people who each member is and what position each person holds. Each member gets a triangle piece of paper to decorate, then all the pieces will be fitted together to form the final display. The triangles are identical and fit together to form a regular polygon. It will look similar to the shape below: If there are 8 council members, what type of polygon will be formed? To achieve this shape, what type of triangles will the individual pieces be? What will be the measures of each of the three angles in each of the triangles? What will be the sum of the measures of the internal angles of the final shape? Redo parts (b) and (c) if the Council decides to include triangles for the two staff advisors, assuming the poster will still form a regular polygon, but now with 10 triangles. An artisan wants to split his equilateral triangular-shaped piece of glass into four equally sized pieces as part of a window design. Explain to him, with a diagram, how to design an inscribed triangle, and show him that the pieces all have equal area. State whether the following statements are true or false, and explain your reasoning. A square is a rectangle. A polygon with 21 sides has 432 possible diagonals. The sum of the measures of the interior angles of a decagon, a ten-sided figure, is . The measures of the exterior angles of a nonagon, a nine-sided figure, have a sum of 360°. Given the following information, give as complete a description of this figure as possible, including the measure of any sides and angles and any terms that can be used to describe the polygon. Briefly, but clearly, discuss another concept that was introduced in this Unit but not specifically addressed in this assessment. As always, support your answer with diagrams and or examples.