Lesson 1
Relationships of Angles
Let’s examine some special angles.
Problem 1
Here are questions about two types of angles.
 Draw a right angle. How do you know it's a right angle? What is its measure in degrees?
 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.

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

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.
 Write a question that could be answered by solving the equation \(100.035d=4\).
 Is 100 a solution of \(100.035d>4\)? Write a question that solving this problem could answer.
Problem 5
Use the distributive property to write an expression that is equivalent to each given expression.
 \(\text3(2x4)\)
 \(0.1(\text90+50a)\)
 \(\text7(\textx9)\)
 \(\frac45(10y+\textx+\text15)\)
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.