4.2: Measuring Angles in Triangles

p. 189-195

Thm 4.1:Triangle Sum Thm

• The sum of the measures of the interior angles of a triangle is 180o.

• mA + mB+ mC=180o

+ + = 180

A

B C

Example 1

• Name Triangle AWE by its angles

4x - 128x + 22

3x +5

A

WE

(3x+5) + ( 8x+22) + (4x-12) = 180mA + mW+ mE=180o

15x + 15 = 180

15x = 165

x = 11

mA = 3(11) +5 = 38o

mW = 8(11)+22 = 110o

mE = 4(11)-12 = 32o

Triangle AWE is obtuse

Example 2

Solve for x .

5x +24

Ans: (5x+24) + (5x+24) + (4x+6) = 180

5x +24 + 5x+ 24 + 4x+6 = 180

14x + 54 = 180

14x = 126

x = 9

Exterior Angles(formed by extending the sides)

(

)) ((

D

E F

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.

• m1=mA+ mB

m1= + 1

A

BC

Example

Exterior angle = 2 nonadjacent angles

3x-10 = (25) + (x+15)

3x-10 = x +40

2x= 50

x = 25

Find every angle measure

40

65115

Exterior angle example

Solve for q

Example

Find the missing angles

70110 110

7040

50

80

60

50

80

Example Find the measure of each numbered angle in

the figure.

Corollary to triangle sum thm

(Corollary- a statement easily proved using a thm.)

* The acute angles of a right triangle are complementary.

A

B C

A is comp. to C