Download 4.2: Angle Measures In Triangles

-QUIZ 3.3 - 3.4
-WARM UP 4.2
-Khan Academy
ESSENTIAL QUESTION
 How
you calculate angle
measures in Triangles?
Triangle Sum Theorem
Theorem 4.2
 The
sum of the measures of the angles of
a triangle is 180
Example 1
Find an Angle Measure
Given mA = 43° and mB = 85°, find mC.
SOLUTION
ANSWER C has a measure of 52°.
Check your solution by substituting 52° for
mC. 43° + 85° + 52° = 180°
Example 2
Find Angle Measures
∆ABC and ∆ABD are right triangles.
Suppose mABD = 35°.
a. Find mDAB.
b. Find mBCD.
SOLUTION
a. mDAB + mABD = 90°
mDAB + 35° – 35° = 90° – 35°
mDAB = 55°
b. mDAB + mBCD = 90°
55° + mBCD = 90°
mBCD = 35°
Checkpoint
Find an Angle Measure
1. Find mA.
ANSWER
65°
ANSWER
75
°
ANSWER
50°
2. Find mB.
3. Find mC.
Exterior Angle Theorem
Theorem 4.2
The measure of an exterior angle of a
triangle is equal to the sum of the
measures of the two nonadjacent interior
angles.
Example
Find an Angle Measure
Given mA = 58° and mC = 72°, find m1.
SOLUTION
m1 = mA + mC
= 58° + 72°
= 130°
ANSWER 1 has a measure of 130°.
Checkpoint
Find an Angle Measure
4. Find m2.
ANSWER
120
°
ANSWER
155
°
5. Find m3.
REVIEW
Classify the triangle by its angles and by its sides.
1.
ANSWER
acute, isosceles
ANSWER
obtuse, isosceles
2.
3. Identify which side is opposite each
angle.
ANSWER
BC is opposite A; AB is opposite C; AC is
opposite B
4. Brittani built a garden bed frame by nailing together
three equal lengths of wood to form a triangle. What
type of triangle did she create?
ANSWER
equilateral or equiangular
 Hw
Worksheet 4.2A