Lesson 4
Solving for Unknown Angles
Problem 1
\(M\) is a point on line segment \(KL\). \(NM\) is a line segment. Select all the equations that represent the relationship between the measures of the angles in the figure.
![M is a point on line segment K L. Segment N M creates two angles, measure a, degrees and b degrees.](https://cms-im.s3.amazonaws.com/dKpGbjgcTi5zugiPN5WT8z7R?response-content-disposition=inline%3B%20filename%3D%227-7.7.4.new.PP.01.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.4.new.PP.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T192403Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=14ef0b3c863181e3d07e3fc1b366455576e079cbcb1578bb93b98429190b1876)
\(a=b\)
\(a+b=90\)
\(b=90-a\)
\(a+b=180\)
\(180-a=b\)
\(180=b-a\)
Solution
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Problem 2
Which equation represents the relationship between the angles in the figure?
![Two rays on the same side of a line meet at a point on the line to form 3 angles, with measure b degrees, 88 degrees, b degrees.](https://cms-im.s3.amazonaws.com/Xfw846G8u7hRtCjAaMT2UWTP?response-content-disposition=inline%3B%20filename%3D%227-7.7.A4.new.PP.05.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.A4.new.PP.05.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T192403Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=8275a547c244b210652dc58c7bb9083f4356b0a23fff531b3a75581c39bbb13f)
\(88+b=90\)
\(88+b=180\)
\(2b+88=90\)
\(2b+88=180\)
Solution
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Problem 3
Segments \(AB\), \(EF\), and \(CD\) intersect at point \(C\), and angle \(ACD\) is a right angle. Find the value of \(g\).
![Segment A, B, segment E F, and segment C D intersect at point C. Clockwise, the endpoints are A, D, E, B, F. Angle A, C D is a right angle. Angle D C E is 53 degrees, angle E C B is g degrees.](https://cms-im.s3.amazonaws.com/LQ3RKdH1ETNirtxGBnkUgwCF?response-content-disposition=inline%3B%20filename%3D%227-7.7.A4.new.PP.06.png%22%3B%20filename%2A%3DUTF-8%27%277-7.7.A4.new.PP.06.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T192403Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=104f12d8acf01a590898a8b78302262fce90433a0824ca61ad4e7c5d08ad39a7)
Solution
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Problem 4
Select all the expressions that are the result of decreasing \(x\) by 80%.
\(\frac{20}{100}x\)
\(x - \frac{80}{100}x\)
\(\frac{100-20}{100}x\)
\(0.80x\)
\((1-0.8)x\)
Solution
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(From Unit 6, Lesson 12.)Problem 5
Andre is solving the equation \(4(x+\frac32)=7\). He says, “I can subtract \(\frac32\) from each side to get \(4x=\frac{11}{2}\) and then divide by 4 to get \(x=\frac{11}{8}\).” Kiran says, “I think you made a mistake.”
- How can Kiran know for sure that Andre’s solution is incorrect?
- Describe Andre’s error and explain how to correct his work.
Solution
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(From Unit 6, Lesson 8.)Problem 6
Solve each equation.
\(\frac17a+\frac34=\frac98\)
\(\frac23+\frac15b=\frac56\)
\(\frac32=\frac43c+\frac23\)
\(0.3d+7.9=9.1\)
\(11.03=8.78+0.02e\)
Solution
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(From Unit 6, Lesson 7.)Problem 7
A train travels at a constant speed for a long distance. Write the two constants of proportionality for the relationship between distance traveled and elapsed time. Explain what each of them means.
time elapsed (hr) | distance (mi) |
---|---|
1.2 | 54 |
3 | 135 |
4 | 180 |
Solution
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(From Unit 2, Lesson 5.)