Question bank: Right and Non-Right Angles

In the Geometry class, teacher João decided to teach about right and non-right angles using everyday shapes. He showed the students a figure of a rectangular window and explained that the vertical and horizontal lines forming the window are perpendicular, which means they meet to form four right angles. Then, he brought a photograph of a park with an oval-shaped lake and asked the students how many right angles a shape like that has, leading them to think about the characteristics of shapes and the relationship between angles. Considering the learning about right and non-right angles and the observation of the presented geometric shapes, how many right angles does an oval-shaped lake have? Also, describe how you reached this conclusion.

In the classroom, teacher Joana brought several drawings of geometric shapes for the students to observe. Among them, there was a pentagon and a triangle. She asked the children to count how many right angles and how many non-right angles they found in each figure. The pentagon is a polygon with five sides and the triangle is a polygon with three sides. When the children counted, they found out that the pentagon has 0 right angles, while the triangle has 3 right angles. Based on what they learned about right and non-right angles, explain why a pentagon has no right angles and why a triangle can have right angles. Also, justify how you arrived at the result found for each figure.

In an Arts class, the 4th-grade students are creating mosaics with simple geometric shapes. Sofia decided to use only squares and rectangles for her mosaic. She wants to ensure that the angles of her mosaic are all right angles to make it well-aligned. After creating a figure, she mentions that there are 12 right angles and some others that are not right angles. Considering that her figure is a square mosaic with a rectangular strip glued to one of its longer edges, how many non-right angles did Sofia add to her mosaic?

In a Math class, students were challenged to identify right and non-right angles in different figures. João has a drawing of a garden where the paths form various types of angles in relation to the flower beds. He knows that a right angle is formed by two perpendicular lines, and that a non-right angle can be acute (smaller than a right angle) or obtuse (larger than a right angle, but smaller than 180 degrees). João wants to know how many right and non-right angles (acute and obtuse) exist in the drawing of the garden. Given that the garden is completely composed of paths that intersect at flower beds, and that he has already identified a perfect square with 4 right angles, help João determine the total number of right and non-right angles in the garden drawing.

When we look at geometric figures, we can find lines that intersect and form what we call angles. Some angles have a special size and we call them right angles, which are like the corner of a book or the plus sign. Angles that are not right angles can be smaller or larger than a right angle. Now, think about the drawings you have seen or even in your notebooks and math books. Describe a figure that you know that has a right angle and an angle that is not right, and tell us how many right angles and how many non-right angles this figure has.