Lesson 56 & 57

Angles in Circles

Ideal Gas Laws

Key Points for Circles

• central angles:– angle with vertex on center of circle– equal to the measure of its arc

• inscribed angles:– angle with vertex on the circle– equal to half the measure of its arc

Key Points for Circles

• if two lines intersect inside a circle:– measure of the angles formed are equal to

half the sum of the measures of the intercepted arcs

• if two lines intersect outside a circle:– measure of the angle formed equals half the

difference of the measures of the intercepted arcs

Example 1

• Find x.

60

x

x

80

Example 2

• Find x.

x

60

80

Example 3

• Find x.

x20

70

Example 4

• Find x. 280

80

x

Ideal Gas Laws

• describes the hypothetical behavior of a gas under ideal conditions

• we’re using these specifically for their algebraic purposes, so you won’t need to know all of the different gas laws

2

22

1

11

T

VP

T

VP

Example 57.1

• Four liters of an ideal gas at a temperature of 800 Kelvin had a pressure of 100 newtons per square meter. If the volume were increased to 10 liters and the temperature reduced to 600 Kelvin, what would the pressure be?

Example 57.2

• The initial pressure of a quantity of an ideal gas was 400 Newtons per square meter and the initial temperature was 1200 Kelvin. The volume was held constant. What was the pressure if the temperature was decreased to 900 Kelvin?

Example 57.3

• The temperature of a quantity of ideal gas was held constant in an experiment. The original pressure was 7 atmospheres and the original volume was 42 liters. If the volume was reduced to 10 liters, what was the final pressure?

Homework

• P.S. 57

• 1-10 all, 12 – 30 even