Lesson 4

\(M\) 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.

\(a=b\)

\(a+b=90\)

\(b=90-a\)

\(a+b=180\)

\(180-a=b\)

\(180=b-a\)

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

\(88+b=90\)

\(88+b=180\)

\(2b+88=90\)

\(2b+88=180\)

Segments \(AB\), \(EF\), and \(CD\) intersect at point \(C\), and angle \(ACD\) is a right angle. Find the value of \(g\).

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

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

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

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

\(0.80x\)

\((1-0.8)x\)

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.

Solve each equation.

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.