Lesson 4

Solving for Unknown Angles

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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.
A:

\(a=b\)

B:

\(a+b=90\)

C:

\(b=90-a\)

D:

\(a+b=180\)

E:

\(180-a=b\)

F:

\(180=b-a\)

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.
A:

\(88+b=90\)

B:

\(88+b=180\)

C:

\(2b+88=90\)

D:

\(2b+88=180\)

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.

Solution

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Problem 4

Select all the expressions that are the result of decreasing \(x\) by 80%.

A:

\(\frac{20}{100}x\)

B:

\(x - \frac{80}{100}x\)

C:

\(\frac{100-20}{100}x\)

D:

\(0.80x\)

E:

\((1-0.8)x\)

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.”

  1. How can Kiran know for sure that Andre’s solution is incorrect?
  2. 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.)