1. Finding Angle Measures with Equations

2. Solve for x 1. Identify the Angle Relationship
2. Set up an equation based on the angle relationship.
3. Solve for x
4. Once you know x, fill in the value for x in the expression to find the missing measure.
5. Find the remaining angle measures.

3. Solve for x 14x - 2 = 13x + 6 14x - 2 = 13x + 6 Now Solve for x -13x
110 70
These angles are Vertical Angles. Vertical Angles are Congruent. So you can set up your problem like this: 70
110
110 70 70
110
14x - 2 = 13x + 6
14x - 2 = 13x + 6
Now Solve for x
-13x
-13x
Once you know x, fill in the value for x in the expression to find the missing measure.
x - 2 = 6 +2 +2
x = 8
14(8) - 2 = 110
Find the remaining angle measures.

4. Solve for x 42x + 4 = 44x - 2 42x + 4 = 44x - 2 -42x -42x
130 50
These angles are Vertical Angles. Vertical Angles are Congruent. So you can set up your problem like this: 50
130
130 50 50
130
42x + 4 = 44x - 2
42x + 4 = 44x - 2
-42x
-42x
Now Solve for x
4 = 2x - 2 +2 +2
Once you know x, fill in the value for x in the expression to find the missing measure.
6 = 2x
3 = x
44(3) - 2 = 130
Find the remaining angle measures.

5. Solve for x 16x – 1 + 85 = 180 16x – 1 + 85 = 180 Now Solve for x
These angles are Supplementary Angles. Supplementary Angles add up to 180°. So you can set up your problem like this: 95 85 85 95 95 85 95
16x – = 180
16x – = 180
Now Solve for x
Combine
Once you know x, fill in the value for x in the expression to find the missing measure.
16x + 84 = 180
-84
-84
16x = 96
16(6) – 1 = 95
Find the remaining angle measures.
x = 6

6. Solve for x 8x – 10 = 7x 8x – 10 = 7x -8x -8x Now Solve for x -10 = -x
These angles are Alternate Interior Angles. Alternate Interior Angles are Congruent. So you can set up your problem like this: 70
110
110 70 70
110
110 70
8x – 10 = 7x
8x – 10 = 7x
-8x
-8x
Now Solve for x
-10 = -x
Once you know x, fill in the value for x in the expression to find the missing measure.
10 = x
8(10) - 10 = 70
Find the remaining angle measures.

7. Solve for x x + 67 = 60 x + 67 = 60 -67 -67 Now Solve for x x = -7
120
These angles are Alternate Exterior Angles. Alternate Exterior Angles are Congruent. So you can set up your problem like this: 60
120
120 60
120 60
x + 67 = 60
x + 67 = 60
-67
-67
Now Solve for x
x = -7
Once you know x, fill in the value for x in the expression to find the missing measure.
(-7) + 67 = 60
Find the remaining angle measures.

8. Now you try!

9. Now you try!

10. Now you try!

11. Now you try!

12. Homework Time !