Lesson 5: Practice Problems

Problem 1

Segments $A B$ , $D C$ , and $E C$ intersect at point $C$ . Angle $D C E$ measures $148^{\circ}$ . Find the value of $x$ .

Horizontal line AB with center C. Line segment DC and EC intersect at point C. Angle DCE is 148 degrees. Angle BCE is marked as x.

Problem 2

Line $ℓ$ is perpendicular to line $m$ . Find the value of $x$ and $w$ .

Straight line m is intersected by perpendicular line l with two other lines intersecting at same point. Angles are 19, x, w, 138, unmarked, 90 degrees.

Problem 3

If you knew that two angles were complementary and were given the measure of one of those angles, would you be able to find the measure of the other angle? Explain your reasoning.

Problem 4 From Unit 6 Lesson 15

For each inequality, decide whether the solution is represented by $x < 4.5$ or $x > 4.5$ .

$- 24 > - 6 (x - 0.5)$
$- 8 x + 6 > - 30$
$- 2 (x + 3.2) < - 15.4$

Problem 5 From Unit 4 Lesson 2

A runner ran $\frac{2}{3}$ of a 5 kilometer race in 21 minutes. They ran the entire race at a constant speed.

How long did it take to run the entire race?
How many minutes did it take to run 1 kilometer?

Problem 6 From Unit 6 Lesson 12

Jada, Elena, and Lin walked a total of 37 miles last week. Jada walked 4 more miles than Elena, and Lin walked 2 more miles than Jada. The diagram represents this situation:

Three tape diagrams are labeled “Elena”, “Jada,” and “Lin.” Elena’s tape diagram is of 1 part labeled m. Jada’s tape diagram is partitioned into 2 parts labeled m and 4. Lin’s tape diagram is partitioned into 3 parts labeled m, 4, and 2. A brace is drawn that contains of all 3 diagrams and is labeled 37.

Find the number of miles that they each walked. Explain or show your reasoning.

Problem 7 From Unit 6 Lesson 19

Select all the expressions that are equivalent to $- 36 x + 54 y - 90$ .

$- 9 (4 x - 6 y - 10)$
$- 18 (2 x - 3 y + 5)$
$- 6 (6 x + 9 y - 15)$
$18 (- 2 x + 3 y - 5)$
$- 2 (18 x - 27 y + 45)$
$2 (- 18 x + 54 y - 90)$