Lesson plan

In this lesson, students will learn how to find the missing angle measure of a triangle. Students will review angle relationships they already know. Then, students will work together to determine the relationships between the angles of a triangle to help them find the missing angle. You can expect this lesson with additional practice to take one `45`-minute class period.

Grade 8

Triangle Theorems

8.G.A.5

Step-by-step help

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Students will be able to find the missing angle measure of a triangle.

- Teacher slideshow
- Online Practice

With this first example, give students the opportunity to think about what they already know that could help them find the missing angle measure of the triangle. Allow students individual time to process the information and then have them share their thoughts to help support student discussions.

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Students should ideally recognize the right angle and recall that triangle angles add up to `180`. Allow students to explain their reasoning when reviewing. It may also help to remind students that it is okay to be incorrect, but they should at least try and come up with something that could help them solve the problem.

Give one more problem where they find the missing angle in a triangle. Since you’ve already discussed how the sum of the angle measure is `180^\circ`, students should be able to reason that `x = 93`.

With the next example, students should be more familiar with what information they will need to focus on to find the missing angle measure of the triangle. Allow students some time to try to solve the problem, and encourage them to work with a partner to check their work.

Students may be confused because of the algebraic expression. Remind students that the angles will still have a sum of `180`. Although some students may write an equation to find `y` directly `(y + 6 + 97 + 42 = 180)`, it is more likely that students will break it into separate parts:

- Adds `97` and `42`. Then subtracts from `180`.
- Subtracts each known angle individually (example: `180-97 = 83, 83-42 = 41`)

- Sets up an equation, like `y + 6 = 41`
- Recognizes the whole angle is `41`, so they need to subtract `41-6` to find `y`.

With the next example, give students an opportunity to try the problem on their own and check it with a partner. Some students may not immediately recognize the right angle, so it will be beneficial for you to walk around and listen to students’ conversations regarding the information given. Remind students of the warm up if needed!

Through student or class discussions, students should be able to explain what the sum of the measures of the two algebraic angles are. Students should be able to solve for `z` using their reasoning skills; however, students may not immediately write an equation. If students are stuck, ask them how they can represent the sum of the two angles in two different ways to help guide them to `4z + 6z = 90` if needed.

To help students practice finding the missing angle measure of a triangle when there is not an image, have students recreate this table on a notecard or piece of paper. Explain to students that they will be creating their own triangles by coming up with angle measures. Encourage them to think about what the key idea behind this is. Students should be talking about how the sum of the `3` angle measures needs to be `180` degrees!

Have students work together to find the value of the variable for each row. Once students have their values, they can plug them back in to check their work!

After you’ve completed the examples with the whole class, it’s time for some independent practice! ByteLearn gives you access to tons of practice problems for finding the missing angle measure of a triangle. Check out the online practice and assign to your students for classwork and/or homework!

Finding the Missing Angle Measure of a Triangle Practice

Problem 1 of 5

<p>What is the value of `x`?</p><UiTriangleV2 data-props='{ "options": { "cell_size": 15, "rows": 14, "columns": 4, "padding": 2, "xOffset": -5, "yOffset": 2 }, "scale_factor": 10, "rotation_angle": 80, "vertex": { "top": { "label": " ", "angle": 31 }, "left": { "label": " ", "angle": 126, "labelYOffset": 2 }, "right": { "label": " ", "angle": 23 } }, "sides": { "base": {}, "left": {}, "right": {} }, "arcs": [ { "position": "top", "labelXOffset": 0, "labelYOffset": 5, "label": "x°" }, { "position": "right", "labelYOffset": -12, "labelXOffset": 5, "label": "23°" }, { "position": "left", "labelYOffset": -8, "labelXOffset": -18, "label": "126°" } ], "background_color": "white", "border_color": "black"}'></UiTriangleV2>

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