180 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 and supplementary angles.

Media
HW / #126
Spiral Review #31
WKSP

Supplementary Angles

A line holds . The sum of all angles creating a line is .

ExampleNon-Example

If the sum of the measurements of two angles is 180, then the angles are . One angle is said to be the of the other angle.

ExampleNon-Example

Remember, the sum of two supplementary angles 180. That means an is formed.

Example 1:

Write an equation for the angle relationship in the diagram and solve for x.

Example 2:

The measure of a supplement of an angle is 6 more than twice the measure of the angle. Find the two angles.

Exercise:

1. / The ratio of the measurement of an angle to its supplement is 3:5. Find the angle and its supplement.
2. / Set up and solve an equation to find the value of x. Find the measurement of AOB and of BOC.

3. / Set up and solve an equation to find the value of k.

Angles on a Line

Example 1:

Two rays have a common vertex on a line. Set up and solve an equation to find the value of z. Find the measurements of AYC and DYB.

Example 2:

Three lines meet at a point. Set up and solve an equation to find the value of a.

Exercise:

4. / Two lines meet at the vertex of a ray. Set up and solve an equation to find the value of c.

5. / The ratio of the measures of three adjacent angles on a line is 3:4:5. Find the measures of the three angles.
6. / Two lines meet at the common vertex of two rays; the measurement of AOF = 134. Set up and solve an equation to find the value of x and y.

Look Out!

To determine the measurement of an unknown angle, you must first identify the angle relationship(s) then model the relationship with an equation.

Example:

Two lines meet at the common vertex of two rays. Set up and solve the appropriate equations for m and n.

Exercise

7. / Two lines meet at the common vertex of a ray. Set up and solve the appropriate equations to determine x and y.

8. / Two lines meet at the common vertex of two rays. Set up and solve an appropriate equation for x and y.

9. / Two lines meet at the common vertex of two rays. Set up and solve an equation to find the values of x and y.

Name: ______Date: ______

Pre-AlgebraExit Ticket

Find the measurements of BAC and DAE

Name: ______Date: ______

Pre-AlgebraExit Ticket

Find the measurements of BAC and DAE

Name: ______Date: ______

Pre-AlgebraHW #126

1. / Set up and solve the appropriate equations for s and t.

2. / The measurement of the supplement of an angle is 39 more than half the angle. Find the measurement of the angle and its supplement.

Review

3. / In a pair of complementary angles, the measurement of the larger angle is three times that of the smaller angle. Find the measurements of the two angles.
4. / What is the y-intercept of the equation y = 5x – 1?
5. / Solve for k: