Answer:
1. a) 3x + 21 = 6x - 60
b) x = 27
c) angle measure = 102º
2. a) 12x - 18 = 8x + 10
b) x = 7
c) angle measure = 66º
3. a) 7x + 9 + 5x + 3 = 180 (simplified: 12x + 12 = 180)
b) x = 14
c) 107º; 73º
4. a) 3x + 10 + 3x -28 = 180 (simplified: 6x -18 = 180)
b) x = 33
c) 109º; 71º
5. a) 12x + 15 = 15x
b) x = 5
c) 75º
Step-by-step explanation:
1. a) they're the same angle so set them equal to each other: 3x + 21 = 6x - 60
b) solve from the equation above
3x + 21 = 6x - 60 subtract 3x from both sides
21 = 3x - 60 add 60 to both sides
81 = 3x divide both sides by 3
x = 27
c) plug back into each equation (they should be the same, but do both just to check)
3(27) + 21 = 81 +21 = 102º
6(27) - 60 = 162 - 60 = 102º
2. a) again, they're the same angle measure so set them equal to each other: 12x - 18 = 8x + 10
b) solve the equation for x
12x - 18 = 8x + 10 subtract 8x from both sides
4x - 18 = 10 add 18 from both sides
4x = 28 divide both sides by 4
x = 7
c) plug back into each equation (they should be the same, but do both just to check)
12(7) - 18 = 84 - 18 = 66º
8(7) + 10 = 56 + 10 = 66º
3. a) the sum of the two angles is 180º so 7x + 9 + 5x + 3 = 180
if you want the equation simplified: 12x +12 = 180
b) solve for x, i will be using the simplified equation
12x + 12 = 180 subtract 12 from both sides
12x = 168 divide both sides by 12
x = 14
c) plug into each equation to get the two angle measures
7(14) + 9 = 98 + 9 = 107º
5(14) + 3 = 70 + 3 = 73º
4. a) the sum of the two angles is 180º so 3x + 10 + 3x -28 = 180
if you want it simplified: 6x -18 = 180
b) solve for x, i will be using the simplified equation
6x - 18 = 180 add 18 to both sides
6x = 198 divide both sides by 6
x = 33
c) plug into each equation to get the two angle measures
3(33) + 10 = 99 + 10 = 109º
3(33) - 28 = 99 - 28 = 71º
5. a) they're the same angle measure so set them equal to each other: 12x + 15 = 15x
b) solve for x with the equation above
12x + 15 = 15x subtract 12x from both sides
15 = 3x divide both sides by 3
x = 5
c) plug back into each equation (they should be the same, but do both just to check)
12(5) + 15 = 60 + 15 = 75º
15(5) = 75º
