1. WARM UP What is the sum of the angle measures of each triangle?
Classify each triangle by its angles and side lengths
What is the sum of the angle measures of each triangle?

2. Section 4.2 Angle measures of Triangles

3. Objective
SWBAT find angle measures in triangles.

4. 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°

5. 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° °
m <C = 52 °

6. Find an angle measure
ABC and ABD are right triangles. Suppose m<ABD=35°. Find m < DAB.
Find m < BCD
m < DAB + m < BCD = 90 °
m < DAB + m <ABC = 90 °
m < DAB + 35° = 90 °
55° + m < BCD = 90 °
- 35° °
- 55° °
m <BCD = 35 °
m < DAB = 55 °

7. YOU TRY
m <A = 65 °
m <B = 75 °
m <C = 50 °

8. 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

9. 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

10. Find an angle measure
Given m < A = 58° and m < C = 72°, find m < 1.
m < 1 = m < A + m < C
= 58° + 72°
= 130°

11. Find an angle measure Find the value of x.C
m < C = m < A + m < B B
136 ° = 94° + x
-94° °
42° = x

12. You Try!
m<2 = 120°
m<3 = 155°
m<4 = 113°

13. Using algebra Find the value of x m< A + m<B + m<C = 180 °
x + 2x + 2x + 15 = 180 °
5x + 15 = 180 °
5x = 165 °
__ ___
5 5
x = 33°

14. Using algebra Find the value of x m< A + m<C = m<B
___ ___
6 6
20° = x

15. You try
Find the value of x
x = 16