Lesson 1

Relationships of Angles

Let’s examine some special 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.

A diagram composed of 4 octagons with the same measure.  They are arranged so that they each touch two others and form a center in the shape of a square.

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.
(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. \(\frac45(10y+\text-x+\text-15)\)
(From Unit 6, Lesson 18.)

Problem 6

Lin’s puppy is gaining weight at a rate of 0.125 pounds per day.  Describe the weight gain in days per pound.

(From Unit 2, Lesson 3.)