Transcript Lesson 3-5: Angles of a Triangle

Lesson 3-5: Angles of a Triangle
Today’s Goals:
1. What is the sum of the angles of a
triangle?
2. What are exterior and remote interior
angles of a triangle and how are they
related?
3. How can I solve for x using these angle
relationships?
Activity: What is the sum of the
3 angle measures of a triangle?
Directions:
1. Label each angle of your
triangle (1, 2, and 3)
1.
2.
Cut the triangle into 3 pieces so
that the angles are separated.
Connect the labeled angles so
that they are adjacent. What is
the sum?
3-5 Notes:
Triangle Angle Sum Theorem
* The sum of the measures of
the angles of a triangle is
180o.
1
2
m1  m2  m3  180
3
Example 1
What are the values of x, y, & z?
Example 2
Solve for x and find the
missing angle measures.
89o
7x – 1
5x + 8
Vocabulary


Exterior Angle of a polygon- an
angle formed by extending the side
of a polygon.
Remote Interior Angles – the two
interior angles that are NOT adjacent
to the exterior angle
Example 3
What are the measures of angle 1
and angle 2?
Shortcut!
Triangle Exterior Angle Theorem
The measure of an exterior angle
of a triangle equals the sum of
the measures of its 2 remote
interior angles.
Section 3-4 in a Nutshell
1. If 2 lines are parallel to the
same line, then they are parallel
to each other.
2. If 2 lines are perpendicular to
the same line then they are
parallel to each other.
3. If 2 lines are parallel and the
transversal is perpendicular to
one line, it is perpendicular to
the other.
3-5 Classwork: solve for the variables.