7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
Ex 1:
Step 1: All angles in a triangle must add up to 180°. Write an
algebraic equation & solve.
Checks for Example 1:
1
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
2
Ex 2:
Step 1: What do we know about the measure of all 3 angles inside of
a triangle? All 3 angles add up to 180°
Step 2: Write an algebraic equation & solve:
Checks for Example 2:
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
3
Ex 3:
Step 1: What do we know about the measure of all 3 angles inside of
a triangle? All 3 angles add up to 180°
Step 2: Write an algebraic equation & solve for x:
NOT DONE YET!!!
Step 3: Instruction says to find measure of angle A.
Plug in -10 for x.
angle A =
angle A = 45 + -10
45-10
angle A = 35°
Checks for Example 3:
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
4
Ex 4:
?
Step 1: What do we know about Linear-Paired or Supplementary
Angles? Both angles add up to 180°
Step 2: Write an algebraic equation & solve for x:
?
20°
Step 3: Find the 3rd angle of the triangle.
What do we know about the measure of all 3 angles inside
of a triangle? All 3 angles add up to 180°
20°
50°
Step 4: The ? and 50° are what kind of angles?
Vertical Angles
Vertical angles are
? must = 50°
ANSWER = 50°
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
Checks for Example 4:
5
Hint: Stat by looking for vertical
angles or linear pairs.
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
6
Ex 5:
x
Step 1: Find all angles inside triangle.
24° and x are what type of angles?
Vertical angles.
What do we know about vertical angles?
They are
(congruent).
x = 24°
24°
x
132° and x are what type of angles?
Linear Pair
What do we know about Linear-Paired angles?
They add up to 180°
24°
48°
x
All angles in a triangle must add up to 180°.
Write an algebraic equation & solve.
24°
48°
108°
Step 2: To find ? (answer), what do we know about Linear-Paired angles?
They add up to 180°. Write an algebraic equation & solve.
ANSWER
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
Checks for Example 5:
7
Hint: Stat by looking for vertical
angles or linear pairs.
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
Ex 6:
Step 1: Which of the two triangles can we solve right away?
Bottom or top triangle?
BOTTOM triangle
It only has one missing angle.
?
Step 2: Write an algebraic equation and solve bottom triangle.
130°
Step 3: What do we know about vertical or opposite angles?
They are congruent (have equal measure).
Fill in the missing vertical angle:
130°
130°
Step 4: Find the missing angle in the top triangle by writing an
algebraic equation & solving for x.
ANSWER
8
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
9
Ex 7:
Step 1: Which of the two triangles can we solve?
Left or right triangle?
LEFT triangle
It only has one missing angle.
?
Step 2: Write an algebraic equation and solve bottom triangle.
70°
Step 3: What do we know about LINEAR PAIRED or supplementary
angles?
They add up to 180°.
Write an algebraic equation for the LINEAR PAIRS and solve:
70°
41°
Step 4: Find the missing angle of triangle on right by writing an
algebraic equation & solving for x.
ANSWER
88°
70°
41°
7-2 Triangle Angle-Sum Theorem_p1-10.notebook
7-2 Triangle Angle-Sum Theorem
10
Checks for Examples 6 & 7:
ANSWER
ANSWER