In middle school, children learn to identify angle pairs, including supplementary, complementary, vertical, and adjacent angles. They then learn to use the relationships of angle pairs to find angle measures.
There are plenty of ways in which math teachers and homeschooling parents can help children become proficient in identifying angle pairs and solving angle-related equations. In this article, we’ve compiled a few tips on teaching angle pairs. Read on to learn more.
Angle Pairs Definition and Types
The first thing to do when teaching angle pairs is to define what this concept is. Explain to children that angle pairs are simply two angles.
Explain that by using our previous knowledge of angles, coupled with our knowledge of traits of parallel lines, we can explore the relations between angle pairs, that is, identify whether two angles are complementary, supplementary, congruent, vertical, adjacent angles or, a linear pair of angles.
You can start by describing adjacent angles. These are two angles with a common vertex and a common side, but with no interior points in common. Use the whiteboard to draw a pair of adjacent angles as an example.
Linear angles refer to two angles that are adjacent and whose non-common sides are opposite rays. Illustrate linear angles on the whiteboard. Point out that the measures of two angles of a linear pair always add up to 180 degrees.
Two angles are said to be complementary if the sum of their measures adds up to 90 degrees. Complementary angles can form perpendicular lines or they can be two separate angles. Demonstrate what complementary angles look like on the whiteboard.
Introduce supplementary angles right after complementary angles, as these are similar. Explain that we also define supplementary angles according to the sum of their degree measures, the difference being that the sum of the measures of supplementary angles is 180 degrees.
Don’t forget to highlight the distinction between supplementary angles and linear angles. While the measures of both types of angle pairs add up to 180 degrees, for two angles to qualify as linear, they must also be adjacent. Show an example of supplementary angles on the whiteboard.
Congruent angle pairs are angles that have the same degree measure. In other words, they have the same angle (in degrees or radians). Congruent angles don’t have to point in the same direction or be on same-sized lines. Provide an example of congruent angles on the whiteboard.
Two angles are vertical if they are opposite each other when two lines intersect. Vertical angles are always congruent, i.e. they’re congruent. So it’s good to introduce vertical angles right after you’ve explained what congruent angles are. Don’t forget to illustrate them on the whiteboard.
Finding Angle Measures
Now you can show students how they can use this newly acquired knowledge about angle pairs in multi-step problems to write and solve equations when there’s an unknown angle in a given figure.
For example, give an angle pair-related problem, such as the following:
‘Find the measure of an angle and its complement, if one angle measures 38 degrees more than the other’.
First illustrate how we can present this word problem in math terms:
m∠1 = x; m ∠2 = x + 38
m∠1 = ?; m∠2 = ?
Point out that ‘m’, in this case, stands for the measure of the angles.
Now you can explain that we’ll start by inferring the information we know from the word problem. We know that the two angles are complementary since the statement asks us to find the measure of an angle and its complement.
So we’ll use this knowledge to write an equation and then solve it. Remind students that the sum of the measures of complementary angles is 90 degrees. In other words, we’ll have the following:
m∠1 + m∠2 = 90
By replacing this with what we identified above, that is, m∠1 = x and m ∠2 = x + 38, we’ll get:
x + x + 38 = 90
or , 2x+ 38 = 90
We’ll then simply shift the 38 to the other side:
2x = 90 – 38
2x = 52
x = 52 ÷ 2
x = 26
In other words:
m∠1 = 26
And since we know that m ∠2 = x + 38:
m ∠2 = 26 + 38
m ∠2 = 64
Activities to Practice Angle Pairs
Once children learn what types of angle pairs exist and are confident in using this knowledge for writing and solving equations, you can introduce different exercises to hone their knowledge. Start with easier exercises and gradually move on to more challenging ones.
A good starting point is this simple Bell-Work Worksheet (Members Only). It contains several exercises of multiple-choice exercises and true and false statements. This resource is suitable for both individual and group practice, so homeschooling parents can also use it.
Angle Pairs’ Pairs
Use this Assignment Worksheet (Members Only), as well as this Exit Quiz Worksheet (Members Only) for this activity. Explain that you’ll be working together in pairs to practice angle pairs! Divide children into pairs of two and hand out the worksheets to each pair.
The members of each pair try to solve the math problems on the worksheets as quickly as possible. Once they’ve solved them, they present their work in front of the class. These worksheets are more challenging, as they also contain exercises on finding angle measures.
Angle Pairs Game
Finally, use this online game by IXL to further practice angle pairs. Make sure there are enough technical devices for each student. This game is suitable for individual work, but you can also use it for group work to stimulate competition between the kids.
You can place students in pairs of two, and let them play on separate devices. As the game measures the score of each student, in the end, they compare their final scores. The person with the biggest number of correct answers wins.
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This article is based on:
Unit 1 – Geometry Basics