2.2 What’s the Relationship? Pg. 8 Complementary, Supplementary, and Vertical Angles

2.2 – What's the Relationship?________________ Complementary, Supplementary, and Vertical Angles Today you will start by looking at angles to identify relationships in a diagram that make angle measures add to a specific number or make angles equal.

Right Adjacent Complementary Angles R One 90° angle 1 2 Angles that share a vertex and side 1 2 Two angles that add to 90°

Straight Linear Pair Supplementary Angles S One 180° angle 1 2 Two adjacent angles that add to 180° 1 two angles that add to 180° 2

Congruent Angles Angle Bisector Vertical Angles A B Angles with same degree A B C D Cuts an angle in half 1 2 Opposite angles that are equal

2.12 – ANGLE MEASURES Name the angle relationship. Then find the missing angles.

a+57= 90 a = 33° complementary

b+41= 180 b = 139° supplementary

c+30= 180 c = 150° supplementary

2.13 – PROVING VERTICAL ANGLES CONGRUENT a. Find the missing angles below.

140° 40° 140°

60° 120°

60° 120° 140° 40° 140° They are congruent

c. Notice that vertical angles appear to always be congruent. This logic is called inductive reasoning because it works for both numbers you plugged in above. Deductive reasoning is a way to show vertical angles are congruent not matter what numbers you use. Below you are given the steps in order to prove that vertical angles are congruent. Your job is to explain why each statement is true. Match the reasons with the given statements.

A. Both add to 180 ° B. Straight angles add to 180 ° C. Subtract y from both sides D. Straight angles add to 180 ° Straight angles add to 180° Both add to 180° Subtract from both sides

2.14 – ANGLE RELATIONSHIPS Use the diagram below. Tell whether the angles are vertical angles, supplementary angles, or neither. Then state if they are congruent, add to something, or have no relationship.

supplementary vertical Add to 180° congruent

vertical supplementary congruent Add to 180°

neither none

2.15 – CONGRUENT ANGLES Use the diagram to complete each statement.

2.16 – CONGRUENT ANGLES Find each indicated angle.

15° 90° 75° 15° 90°

106° 74° 106° 67° 90° 67° 23°

2.17 –ANGLES RELATIONSHIPS Find a special relationship between some of the angles, and use that relationship to write an equation. Solve the equation for the variable, then use that variable to find the missing measurement.

supplementary 4x+6+ 11x-6= x = 180 x = 12 11(12)-6 126°

Angle bisector 4x – 5= 3x + 2 x – 5 = 2 x = 7 3(7)+2 23°

Complementary 2x-4+ x+7= 90 3x + 3 = 90 3x = 87 x = °

Vertical 9x + 7= 5x x + 7 = 67 4x = 60 x = 15 15°

Supplementary 21x-3+ 5x+1= x – 2 = x = 182 x = 7 7°

Supplementary 4y+ 17y-9= y – 9 = y = 189 y = 9 7° 9°

Supplementary 6x-11+ 2x-9= 180 8x – 20 = 180 8x = 200 x = 25 25°

Supplementary 25° 6(25) Vertical 20y +19= y = 120 y = 6 6°