Stand Quietly

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

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?

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

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.

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

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 –117 p = 63

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 –85 m = 95

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

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 –62 c = 118

Example 5 Find the angle measures in the scalene triangle. 2x° + 3x° + 5x° = 180° Triangle Sum Theorem 10x = 180 Simplify. 10 10 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°.

Example 6 Find the angle measures in the scalene triangle. 3x° + 7x° + 10x° = 180° Triangle Sum Theorem 20x = 180 Simplify. 20 20 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°

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: 56+93+31 = 180° 4x + 56= 180 4x = 124 x = 31

2x+15 = 2(15)+15 = 45° 3x= 3 15 =45° Check work: 45+45+90 = 180° Example 8 2x + 15 + 3x + 90 = 180 2x + 15 5x + 105 = 180 5x = 75 3x x = 15 2x+15 = 2(15)+15 = 45° 3x= 3 15 =45° Check work: 45+45+90 = 180°