90 Degrees

Pre - Requisite
Standard / 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
CC Lesson / 7.6.1: Complementary and Supplementary Angles
7.6.2-4: Solve for Unknown Angles using Equations
7.3.10 Angle Problems and Solving Equations
Student Learning Goal /
  • Students solve for unknown angles in word problems and in diagrams involving complementary angles.

Media
HW / #125
Spiral Review #31
WKSP

An Angle

The symbol used to represent the word ‘angle’ is

1 is also known as ______or ______.

If you know the measurement of the angle, it is noted as ___1.

Adjacent Angles

Two angles are if they share a common vertex and a common ray. The angles do not overlap!

ExampleNon-Example

Example:

The sum of the measures of two adjacent angles is 72. The ratio of the smaller angle to the larger angle is 1:3. Find the measures of each angle.

Exercise:

1. / The sum of two adjacent angles is 58. If one angle is 32, what is the other angle?
2. / The ratio of two angles is 2:3. The sum of the two adjacent angles is 35. Find the measure of both angles.
3. / The sum of three adjacent angles is 60. If each angle is 10 more than the prior angle, what is the measure of each angle?

Complementary Angles

If the sum of the measurements of two angles is 90, then the angles are . One angle is said to be the of the other angle.

ExampleNon-Example

Remember, the sum of two complementary angles 90. That means an is formed.

Example:

The measurement of an angle is the measurement of its complement. Find the measurement of the angle.

Exercise:

4. / The ratio of the measurement of an angle to its complement is 1:2. Find the angle and its complement
5. / Four times the measurement of an angle is the complement of the angle. Find the measurement of the angle and its complement.
6. / The measure of a complement of an angle is 32 more than three times the angle. Find the two angles.

Right Angles

If the two complementary angles are adjacent, they create a ______angle.

Example 1:

The ratio of GFH to EFH is 2:3. Find the measures of GFH and EFH.

If two intersecting lines create 90 angles, the lines are said to be to each other.

ExampleNon-Example

Example 2:

Two lines meet at the common vertex of two rays. Set up and solve the appropriate equations to determine x and y.

Exercise:

7. / Set up and solve an equation to find the value of x. Find the measurements of AOB and BOC.

8. / a. Set up and solve an equation to solve for the value of x.

b. Use the value of x and a relevant angle relationship in the diagram to determine the measure of EAF.
9. / Two lines meet at the common vertex of two rays. Set up and solve an equation to find the values of a andb.

Name: ______Date: ______

Pre-AlgebraExit Ticket

Set up and solve an equation to find the value of x. Find the measurement of AOB and of BOC.

Name: ______Date: ______

Pre-AlgebraExit Ticket

Set up and solve an equation to find the value of x. Find the measurement of AOB and of BOC.


Name: ______Date: ______

Pre-AlgebraHW #125

1. / Find the measure of CAD and DAE.

2. / The measure of the complement of an angle exceeds the measure of the angle by 25%. Find the angle and its complement.

Review

3. / What is the unit rate of $27 in 3 hours?
4. / From the equation y = 2x + 1,
a. state the slope and y-intercept
slope = y-intercept =
b. Graph the equation y = 2x + 1 on the coordinate axis below.

5. / Solve the equation 2x – 5 = 7. Then check your answer.