Lesson 4

Solving for Unknown Angles

Let’s figure out some missing 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.

M is a point on line segment K L. Segment N M creates two angles, measure a, degrees and b degrees.












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.








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.

Problem 4

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




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







(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.
(From Unit 6, Lesson 8.)

Problem 6

Solve each equation.






(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
(From Unit 2, Lesson 5.)