1. Stand Quietly

2. Lesson 7.3 Angle Measures of Triangles
Students will able to use the property of a triangle to find the missing values.

3. Warm-Up #20 (4/13/17)
A Jacket with an original price of $56.70 is discounted 40%. What is the sale price?
A saving account earns 4% annual simple interest. The principal is $1100. What is the balance after 5 years?
Sonja bought a new van for her business. The sticker price on the van was $35,000. Sonja got a 10% discount from that price. Then she had to pay 8% sale tax. What was the total cost of the van including tax?

4. Worksheet: Complementary and Supplementary Angles
Homework (4/13/17)
Worksheet: Complementary and Supplementary Angles

6. Scalene triangles do not have any congruent sides and no congruent angles.
Isosceles triangle has 2 congruent sides and 2 of the angles will also have the same angle measure.
Equilateral triangle has 3 congruent sides and all angles have the measurement of 60 degrees.

7. Triangle Sum Theorem
The sum of the angle measures in a triangle equal 180° 3 2 1
1 + 2 + 3 = 180°

8. Example 1 A. Find p in the acute triangle. 73° + 44° + p° = 180°
Triangle Sum Theorem
73° + 44° + p° = 180°
117 + p = 180
Subtract 117 from both sides.
– –117
p = 63

9. Example 2 62 B. Find m in the obtuse triangle. 23° + 62° + m° = 180°
Triangle Sum Theorem
23° + 62° + m° = 180°
23 m
85 + m = 180
Subtract 85 from both sides.
– –85
m = 95

10. Example 3 A. Find a in the acute triangle. 38° Triangle Sum Theorem
Subtract 126 from both sides.
– –126
a = 54 a°
88°

11. Example 4 B. Find c in the obtuse triangle. c° 24° 38°
Triangle Sum Theorem. c°
24°
38°
24° + 38° + c° = 180°
62 + c = 180
Subtract 62 from both sides.
– –62
c = 118

12. Example 5 Find the angle measures in the scalene triangle.
2x° + 3x° + 5x° = 180°
Triangle Sum Theorem
10x = 180
Simplify.
Divide both sides by 10.
x = 18
The angle labeled 2x° measures 2(18°) = 36°, the angle labeled 3x° measures 3(18°) = 54°, and the angle labeled 5x° measures 5(18°) = 90°.

13. Example 6 Find the angle measures in the scalene triangle.
3x° + 7x° + 10x° = 180°
Triangle Sum Theorem
20x = 180
Simplify.
Divide both sides by 20.
x = 9
10x°
The angle labeled 3x° measures 3(9°) = 27°, the angle labeled 7x° measures 7(9°) = 63°, and the angle labeled 10x° measures 10(9°) = 90°.
3x°
7x°

14. 3x = 3(31) = 93° x= 31° Check work: 56+93+31 = 180° Example 7
We will do algebraic problems using this theorem.
The sum of the angles is 180, so
x + 3x + 56= 180
3x = 3(31) = 93°
x= 31°
Check work:
= 180°
4x + 56= 180
4x = 124
x = 31

15. 2x+15 = 2(15)+15 = 45° 3x= 3 15 =45° Check work: 45+45+90 = 180°
Example 8
2x x + 90 = 180
2x + 15
5x = 180
5x = 75 3x
x = 15
2x+15 = 2(15)+15 = 45°
3x= 3 15 =45°
Check work:
= 180°