# Lesson 1

Relationships of Angles

### Problem 1

Here are questions about two types of angles.

1. Draw a right angle. How do you know it's a right angle? What is its measure in degrees?
2. Draw a straight angle. How do you know it’s a straight angle? What is its measure in degrees?

### Problem 2

An equilateral triangle’s angles each have a measure of 60 degrees.

1. Can you put copies of an equilateral triangle together to form a straight angle? Explain or show your reasoning.

2. Can you put copies of an equilateral triangle together to form a right angle? Explain or show your reasoning.

### Problem 3

Here is a square and some regular octagons.

In this pattern, all of the angles inside the octagons have the same measure. The shape in the center is a square. Find the measure of one of the angles inside one of the octagons.

### Problem 4

The height of the water in a tank decreases by 3.5 cm each day. When the tank is full, the water is 10 m deep. The water tank needs to be refilled when the water height drops below 4 m.

1. Write a question that could be answered by solving the equation $$10-0.035d=4$$.
2. Is 100 a solution of $$10-0.035d>4$$? Write a question that solving this problem could answer.

### Solution

(From Unit 6, Lesson 17.)

### Problem 5

Use the distributive property to write an expression that is equivalent to each given expression.

1. $$\text-3(2x-4)$$
2. $$0.1(\text-90+50a)$$
3. $$\text-7(\text-x-9)$$
4. $$\frac45(10y+\text-x+\text-15)$$