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Lesson Plans on Measuring Angles

Angles, a basic unit of geometry, consist of two lines called arms that connect at a point called the vertex. The distance between the arms is called the measurement of the angle. Though there are more-advanced units for the measurement of angles, degrees are the best unit to use during introductory lessons. Understanding the fundamentals of angles provides the foundation for learning geometric figures such as triangles, which in turn introduce the basic concepts of trigonometry.

Recognizing Angles
- Angles can be divided into right angles, acute angles, obtuse angles and reflex angles. Learning to identify each type on sight allows students to know the degree range for the answer. Right angles, which have straight arms that form an L shape, will always measure 90 degrees, while acute angles, with arms closer together than a right angle and a narrower vertex, will have a measurement between zero and 90 degrees. Obtuse angles are larger, or wider, than right angles and have an answer range of 90 to 180 degrees. The upper boundary is due to the fact that 180 degrees is a straight line. The three angles mentioned thus far will always have their straight arm as the lower arm and the arm that needs to be measured as the upper arm. But reflex angles have the straight arm at the top and the angled arm at the bottom. That's because these angles are larger than 180 and the angled arm has thus traveled all the way around, past the straight-line point.
Measuring Angles
- Instruct students on proper protractor usage. Find the mark halfway across the straightedge bottom of the protractor, and line that up with the vertex of the angle being measured. Note that this positioning should also line up the straight arm with the zero degree mark on the protractor. Trace the path of the angled arm to find what degree number it points through, rounding to the nearest whole number if necessary.
Working With Reflex Angles
- Explain that reflex angles require an extra step since these angles are larger than 180 degrees, which is the upper boundary for the protractor's measurements. Extend the straight arm, which is the upper arm in a reflex angle, to create a straight line. Note that this extension creates a new angle between the line and the angled arm below. Measure this new angle with the protractor. Add the degrees to 180, from the line, to find the total reflex measurement. For example, if the new angle measured 35 degrees, the answer would be 180 + 35 = 215 degrees.
Drawing Angles
- Conclude an introductory coursework on measuring angles by assigning students angles to draw for homework. Show a few examples as a guide, noting that the easiest way to draw most angles is to position the protractor, draw the lower line at zero degrees, make a mark at the other needed angle and use the straight edge of the protractor to draw the second line. Include right angles, acute angles, obtuse angles and reflex angles in the problems.

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