1. Combining Your Knowledge of Angles With Your Ability to Solve Equations You will have to write and solve equations to find values of variables related to angles.

2. a.No. The angles are adjacent but their noncommon sides are not opposite rays. b. Yes. The angles are adjacent and their noncommon sides are opposite rays. c. No. The sides of the angles do not form two pairs of opposite rays. (The left side of angle 3 to the right side of angle 1 does not make a straight line.) d. No. The sides of the angles do not form two pairs of opposite rays. (The left side of angle 2 to the right side of angle 4 does not make a straight line.)

3. Vertical angles will be congruent. Their angles measures will be equal. You can set the two angles equal to each other. Linear Pair angles are supplementary. The sum of the two angles will be 180°. 105 = 2x - 11 78 = 5x - 2 6x + 19 + x = 180

4. Vertical angles will be congruent. Their angles measures will be equal. You can set the two angles equal to each other. Linear Pair angles are supplementary. The sum of the two angles will be 180°. 105 = 2x - 11 116 = 2x 58 = x +11 ÷2 78 = 5x - 2 80 = 5x 16 = x +2 ÷5 6x + 19 + x = 180 7x + 19 = 180 7x = 161 1x = 23 ÷7 -19

5. Corresponding Angles will be congruent because the lines are parallel. This means the red angle 4 will be equal to 125°.

6. These two angles make a linear pair, and will be supplementary. They will add up to 180 x + 15 + 125 = 180 x + 140 = 180 x = 40 -140

8. Linear pair so 67 + x =180 x will equal 113. x and y are Alternate Exterior Angles so they will be congruent. y will also be 113 Vertical angles are equal so y = 109 x and the 109 angle and consecutive interior angles so they will be supplementary. 109 + x = 180 so x will be 71 The red right angle and angle y are Alternate Interior Angles, so they will be congruent. y will equal 90. x and y are a linear pair and will add up to 180. If y is 90 then x must be 90, too.

10. Linear pairs will each add up to 180 180 = y +65180 = x + 80 Corresponding angles are congruent so x = 65. Corresponding angles are congruent so x = 130. Vertical angles are congruent so y = 130 Alternate Exterior angles are congruent so y = 80.

12. Congruent angles that should be set equal to each other: Vertical angles Corresponding Angles (F Property) Alternate Interior Angles (Z Property) Alternate Exterior Angles Supplementary angles that should be added together to equal 180: Linear Pair angles Consecutive or Same-side Interior Angles (C Property) Consecutive or Same-side Exterior Angles