Nonadjacent Angles: IM 7.7.3
[url=https://im.kendallhunt.com/MS/teachers/2/7/3/preparation.html]“Nonadjacent Angles”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson 7.7.3
- IM 7.7.3 Lesson: Nonadjacent Angles
- Practice 7.7.3
- IM 7.7.3 Practice: Nonadjacent Angles
IM 7.7.3 Lesson: Nonadjacent Angles
Given [math]a[/math] and [math]b[/math] are numbers, and [math]a+b=180[/math] , which statements also must be true?
Use any useful tools in the geometry toolkit to identify any pairs of angles in these figures that are complementary or supplementary.
Use a straightedge to draw two intersecting lines. Use a protractor to measure all four angles whose vertex is located at the intersection.
Compare your drawing and measurements to the people in your group. Make a conjecture about the relationships between angle measures at an intersection.
[size=150]Find the measure of the angles in [b]column A[/b]. Your partner will work on the problems in [b]column B[/b]. Check in with your partner after you finish each example. Your answers for each problem number should be the same. If your answers aren’t the same, work together to find the error and correct it.[/size]
Find the measure of the angles in one column.
IM 7.7.3 Practice: Nonadjacent Angles
Two lines intersect. Find the value of [math]b[/math] and [math]c[/math].
In the figure above, angles [math]R[/math] and [math]S[/math] are complementary. Find the measure of angle [math]S[/math].
If two angles are both vertical and supplementary, can we determine the angles? Is it possible to be both vertical and complementary?
If so, can you determine the angles? Explain how you know.
Match the equivalent expression:
[math]5(x+1)-2x+11[/math]
[math]2x+2+x+5[/math]
[math]\frac{\text{-}3}{8}x-9+\frac{5}{8}x+1[/math]
[math]2.06x-5.53+4.98-9.02[/math]
[math]99x+44[/math]
Factor each expression.
[math]15a-13a[/math]
[math]-6x-18y[/math]
[math]36abc+54ad[/math]
[size=150]The directors of a dance show expect many students to participate but don’t yet know how many students will come. The directors need 7 students to work on the technical crew. The rest of the students work on dance routines in groups of 9. For the show to work, they need at least 6 full groups working on dance routines.[/size][br][br]Write and solve an inequality to represent this situation.
Graph the solution on number line.
Write a sentence to the directors about the number of students they need.
[size=150]A small dog gets fed [math]\frac{3}{4[/math] cup of dog food twice a day. [/size][br][br]Using [math]d[/math] for the number of days and [math]f[/math] for the amount of food in cups, write an equation relating the variables.
Use the equation to find how many days a large bag of dog food will last if it contains 210 cups of food.