1. 4.2: Measuring Angles in Trianglesp

2. Thm 4.1:Triangle Sum Thm A B C
The sum of the measures of the interior angles of a triangle is 180o.
mA + mB+ mC=180o
= 180 A B C

3. Example 1 Name Triangle AWE by its angles mA + mW+ mE=180o
(3x+5) + ( 8x+22) + (4x-12) = 180 A
15x + 15 = 180
15x = 165
x = 11
3x +5
mA = 3(11) +5 = 38o
8x + 22
mW = 8(11)+22 = 110o
4x - 12 W
mE = 4(11)-12 = 32o E
Triangle AWE is obtuse

4. Example 2 Solve for x . Ans: (5x+24) + (5x+24) + (4x+6) = 180

5. Exterior Angles (formed by extending the sides))) ((

6. Thm 4.2: Exterior Angles Thm
The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles.
m1=mA+ mB
m1= + A 1 B C

7. Example Find every angle measure Exterior angle = 2 nonadjacent angles65
3x-10 = (25) + (x+15)
3x-10 = x +40
2x= 50
x = 25
115 40

8. Exterior angle example
Solve for q

9. Example
Find the missing angles 80 80 60 40 50 50 70 70

11. Find the measure of each numbered angle in the figure.
Example
Find the measure of each numbered angle in the figure.

12. Corollary to triangle sum thm
(Corollary- a statement easily proved using a thm.)
* The acute angles of a right triangle are complementary. A
A is comp. to C B C