Lesson 4: Practice Problems

Problem 1

$M$ is a point on line segment $K L$ . $N M$ is a line segment. Select all the equations that represent the relationship between the measures of the angles in the figure.

Line KL with point M and a line extending from M to N. Angle KMN is labeled a and NML is labeled b.

$a = b$
$a + b = 90$
$b = 90 - a$
$a + b = 180$
$180 - a = b$
$180 = b - a$

Problem 2

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

A straight line with two line intersecting a point on the line. The three angles formed are b, 88, and b.

$88 + b = 90$
$88 + b = 180$
$2 b + 88 = 90$
$2 b + 88 = 180$

Problem 3

Segments $A B$ , $E F$ , and $C D$ intersect at point $C$ , and angle $A C D$ is a right angle. Find the value of $g$ .

Line AB intersected by lines EF and D all intersecting at point C. ECG is labeled g. DCE is 53 degrees. DCA is 90 degrees.

Problem 4 From Unit 6 Lesson 12

Select all the expressions that are the result of decreasing $x$ by 80%.

$\frac{20}{100} x$
$x - \frac{80}{100} x$
$\frac{100 - 20}{100} x$
$0.80 x$
$(1 - 0.8) x$

Problem 5 From Unit 6 Lesson 8

Andre is solving the equation $4 (x + \frac{3}{2}) = 7$ . He says, “I can subtract $\frac{3}{2}$ from each side to get $4 x = \frac{11}{2}$ 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.

Problem 6 From Unit 6 Lesson 7

Solve each equation.

$\frac{1}{7} a + \frac{3}{4} = \frac{9}{8}$
$\frac{2}{3} + \frac{1}{5} b = \frac{5}{6}$
$\frac{3}{2} = \frac{4}{3} c + \frac{2}{3}$
$0.3 d + 7.9 = 9.1$
$11.03 = 8.78 + 0.02 e$

Problem 7 From Unit 2 Lesson 5

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)
$1.2$	$54$
$3$	$135$
$4$	$180$