# 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.

\(a=b\)

\(a+b=90\)

\(b=90-a\)

\(a+b=180\)

\(180-a=b\)

\(180=b-a\)

### Solution

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### Problem 2

Which equation represents the relationship between the angles in the figure?

\(88+b=90\)

\(88+b=180\)

\(2b+88=90\)

\(2b+88=180\)

### 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 \(g\).

### 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

### 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

### 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

### 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 |