Download Section 4.2 Angle measures of Triangles

WARM UP
Classify each triangle by its angles and side lengths
What is the sum of the angle measures of each triangle?
Section 4.2
Angle measures of
Triangles
Objective
• SWBAT find angle measures in triangles.
triangle sum theorem
The sum of the measures of the angles of a triangle is 180°.
m<A + m <B + m <C = 180°
The acute angles of a right triangle are complementary (90°)
If m <C =90°, then m<A + m<B = 90°
Finding angle measures of a right triangle
Given m<A=43° and m<B=85°, find the m<C
m < A + m <B + m <C = 180 °
43° + 85° + m <C = 180 °
128° + m <C = 180 °
- 128°
- 128 °
m <C = 52 °
Find an angle measure
ABC and ABD are right triangles. Suppose m<ABD=35°.
Find m < DAB.
m < DAB + m <ABC = 90 °
m < DAB + 35° = 90 °
- 35° - 35 °
m < DAB = 55 °
Find m < BCD
m < DAB + m < BCD = 90 °
55° + m < BCD = 90 °
- 55°
- 55 °
m <BCD = 35 °
YOU TRY
m <A = 65 °
m <B = 75 °
m <C = 50 °
Interior and exterior angles
When the three sides of the triangle are extended
other angles are formed.
The three original angles are
the interior angles
The angles that are are
adjacent to the interior angles
are the exterior angles
Exterior angle theorem
The measure of an exterior angle of a triangle is
equal to the sum of the measures of the two
nonadjacent interior angles.
Symbols:
m<1 = m<A + m<B
Find an angle measure
Given m < A = 58° and m < C = 72°, find m < 1.
m<1=m<A +m<C
= 58° + 72°
= 130°
Find an angle measure
A
Find the value of x.
m<C=m<A +m<B
136 ° = 94° + x
-94° -94°
42° = x
C
B
You Try!
m<2 = 120°
m<3 = 155°
m<4 = 113°
Using algebra
Find the value of x
m< A + m<B + m<C = 180 °
x + 2x + 2x + 15 = 180 °
5x + 15 = 180 °
- 15 -15
5x
__ = 165
___ °
5
5
x = 33°
Using algebra
Find the value of x
m< A + m<C = m<B
82° + 38° = 6x
120°
6x
___ = ___
6
6
20° = x
You try
Find the value of x
x = 16