1. 11.2 Angle Theorems for Triangles
What can you conclude about the measures of the angles of a triangle?
The sum of the measures of the interior angles of a triangle is always 180°. The measure of an exterior angle is equal to the sum of its remote interior angles.

2. 180-5x
180-5x 5x
Review

3. 11x° + 4x° = 180° => 15x° = 180° => x =12
BCF = 4(12) AND CFE = 11(12)
4x°
11x°
Review

4. Plug X into Missing Angles
7x°+40° + 3x° = 180°
10x + 40 = 180
10x = 140
x = 14
Plug X into Missing Angles
CFG => 3(14) = 42°
DCF => = 138°
Review

5. Justifying Triangle Sum Theorem
States that for triangle ABC, m<A + m<B + m<C = 180 °
Justifying Triangle Sum Theorem
You can use your knowledge of parallel lines intersected by a transversal, to informally justify the triangle sum theorem.
Pg. 354 in textbook
What angle is alt. int. angle to 4 and 5?
What would be the degrees if you added angles 1, 2 and 3?
180°

6. How many degrees are in a triangle? 180° 63 +42 + x = 180
Example

7. Identifying the theorem of a triangle
Identify the vertices (corners of triangle)
Add measures of angles to equal 180°
x = 180
90 + x = 180
x = 180
X = 90
127 + x = 180
90°
X = 53°
Identifying the theorem of a triangle

8. Vocabulary Interior angle – formed by two sides of the triangle.
Exterior angle – formed by one side of the triangle and the extension of an adjacent angle;
Exterior Angle, when extended, will form a 180° angle.
Remote interior angle – interior angle that is not adjacent to the exterior angle.
Vocabulary

9. 180°
Since we extended the line and created angle 4, the extension created a ___________ angle.
180°

10. 9x+4+4x+1+97=180 13x +102 = 180 13x = 78 => x=6 Example
To find C: Subtract = 97
<A = 9x +4
<B = 4x + 1
<C = 97
A + b + c = 180
9x+4+4x+1+97=180
13x +102 = 180
13x = 78 => x=6
Example

11. 5y+3+4y+8+34 = 180 9y+45=180 9y=135 => y=15 180 -146 34
M = 5(15) + 3; M=78
N = 4(15) + 8; N = 68
= 180

12. CW – pg. 358 # 1-7
HW – 11.2 HRW
CW and HW