# 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:

$$a=b$$

B:

$$a+b=90$$

C:

$$b=90-a$$

D:

$$a+b=180$$

E:

$$180-a=b$$

F:

$$180=b-a$$

### Solution

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### Problem 2

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

A:

$$88+b=90$$

B:

$$88+b=180$$

C:

$$2b+88=90$$

D:

$$2b+88=180$$

### 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%.

A:

$$\frac{20}{100}x$$

B:

$$x - \frac{80}{100}x$$

C:

$$\frac{100-20}{100}x$$

D:

$$0.80x$$

E:

$$(1-0.8)x$$

### Solution

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(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.

### Solution

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(From Unit 6, Lesson 8.)

### 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

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(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

### Solution

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(From Unit 2, Lesson 5.)