360 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 / 7.6.2-4: 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, supplementary, vertical & adjacent angles.

Media
HW / #127
Spiral Review #31
WKSP

Vertical Angles

When two lines intersect, any two non-adjacent angles formed by those lines are called ______angles.

ExampleNon-Example

Vertical angles have measures.

Example 1

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

Example 2

Two lines meet at the common vertex of two rays. Set up and solve an equation to find the value of x. Find the measurements of CAH and EAG.

Exercise:

1. / Two lines meet at a point. Find the values of r, s, and t.

2. / Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. Set up and solve an equation to find the value of t.

3. / Find the measure of x and y.

Angles Around a Point

How many degrees are in a (full) circle?

The sum of all the angles around a point is .

Example:

Set up and solve an equation to find the value of x.

Exercise:

4. / Five rays meet at a common vertex. Set up and solve an equation to find the value of a.

5. / Four rays meet at a common vertex. Set up and solve an equation to find the value of x. Find the mBAC and mDAE.

6. / Write an equation for the angle relationship shown in the figure and solve for b.

Look Out!!

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

Example

Set up and solve an equation to find the value of x.

Exercise:

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

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

9. / Set up and solve an equation to find the value of x.

Name: ______Date: ______

Pre-AlgebraExit Ticket

Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. Set up and solve an equation to find the value of v.

Name: ______Date: ______

Pre-AlgebraExit Ticket

Two lines meet at the vertex of a ray. The ray is perpendicular to one of the lines as shown. Set up and solve an equation to find the value of v.

Name: ______Date: ______

Pre-AlgebraHW #127

1. / Three lines meet at a point; AOF = 144. Set up and solve an equation to determine the value of c.

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

Review

3. / The supplement of the measurement of an angle is 16 less than three times the angle. Find the angle and its supplement.
4. / What is the y-intercept of the graph below?

5. / Write the decimal value of . (NO calculator).