Mathematical Reflections
What are common properties of all polygons?
Polygons are closed shapes that have at least three straight sides, angles and vertices. They are also planar, which means they are 2D. Many shapes are polygons, as long as they don't have intersections or rounded edges. Here are a few examples of polygons and non-polygons.
What does the measure in degrees tell you about an angle?
If it is an angle from a polygon, it can tell you more about that shape. For example, maybe if you knew that a triangle had right angle, you automatically know that the triangle is a right triangle. Also, you can know whether it is obtuse, right, acute or straight without seeing the angle itself.
What are some common benchmark angles?
Benchmarks are angles simpler angles to make, like a 90 degree angle. Here are a few in addition to that. 45 degrees, 180 degrees, 270 degrees, 360 degrees, 30 degrees, 60 degrees. They would be the most popular.
What strategies can be used to find angle measure?
First, I would see whether it is obtuse, acute, right or reflex. This alone can tell you a lot and narrow down options. Then, I would look at the angle and see whether it is close to any benchmark angle that I know of. After I find my benchmark angle, I would look at how close or far the angle in question is from the benchmark. Also, to check my work, I can look at the complementary and supplementary angles. If I estimate the angle is, say 135 degrees, I would look and see if its supplementary angle looked about 45 degrees or not.
To find accurate measurements with tools...
I use protractors. You would put the little circle/dot which is at the middle or bottom of the protractor on the vertice of the angle (where the two lines intersect). Next to the dot, there would be a straight line, which you need to line the side the angle starts counterclockwise from. Then, you would see where the other line it on the protractor. You would need to see which line it lines up with and find out how many degrees that line would be. Once you have determined that, then you have found your answer.
What strategies can be used to find angle measure?
First, I would see whether it is obtuse, acute, right or reflex. This alone can tell you a lot and narrow down options. Then, I would look at the angle and see whether it is close to any benchmark angle that I know of. After I find my benchmark angle, I would look at how close or far the angle in question is from the benchmark. Also, to check my work, I can look at the complementary and supplementary angles. If I estimate the angle is, say 135 degrees, I would look and see if its supplementary angle looked about 45 degrees or not.
To find accurate measurements with tools...
I use protractors. You would put the little circle/dot which is at the middle or bottom of the protractor on the vertice of the angle (where the two lines intersect). Next to the dot, there would be a straight line, which you need to line the side the angle starts counterclockwise from. Then, you would see where the other line it on the protractor. You would need to see which line it lines up with and find out how many degrees that line would be. Once you have determined that, then you have found your answer.
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