1. 70
2. 22
3. 56
4. 16
5. 35
6. 15
7. 260
8. 7
Step-by-step explanation:
Find the value of x in the linear pair. To do so, you have to add both the angles and equal it to 180. Since it's a straight line, it would be 180.
1) The angles are (2x+6) and 34.
1.Set up the equation
(2x + 6) + 34 = 180
2. Combine like terms
2x + (6 + 34) = 180
2x + 40 = 180
3. Get x alone
2x + 40 = 180
2x + 40 (-40) = 180 (-40)
2x = 140
2x (/2) = 140 (/2)
x = 70
70
2) The angles are 5x/2 and 125.
1. Set up the equation
(5x/2) + 125 = 180
2. Combine like terms
5x/2 + 125 = 180
There are no like values because the 2 is a denominator.
3. Get x alone.
5x/2 + 125 (-125) = 180 (-125)
5x/2 = 55
5x/2 (*2) = 55 (*2)
To get the x alone when in a fraction when its the numerator, do reciprocal to get rid of the denominator.
5x = 110
5x (/5) = 110 (/5)
x = 22
22
3) Angles are 2x-3 and 71.
1. Set up the equation
(2x - 3) + 71 = 180
2. Combine like terms
2x + (-3 + 71) = 180
2x + 68 = 180
3. Get x alone
2x + 68 (-68) = 180 (-68)
2x = 112
2x (/2) = 112 (/2)
x = 56
56
4) The angles are (3x + 42) and 90
Well this one is easier than the rest.
You know one side is 90 degrees. Thats a right angle, right?
Well, the other side also has to be a right angle, 90 degrees.
Why? Well, 180 - 90 = 90
So lets set up the equation differently.
3x + 42 = 90
It can be set up like this because you know the angle measurement, you just need x. You can do it the way the previous problems have been set up as well, but keep in mind this is also an option.
2. Solve for x
3x + 42 (-42) = 90 (-42)
3x = 48
3x (/3) = 48 (/3)
x = 16
16
5) The angles are 2x-38 and 148
1. Set up the equation
(2x - 38) + 148 = 180
2. Combine like terms
2x + (-38 + 148) = 180
2x + 110 = 180
2x + 110 (-110) = 180 (-110)
2x = 70
2x (/2) = 70 (/2)
x = 35
35
6) Angles are 100 and (5+5x)
1. 180 - 100
80 will be what your going to se the equation to
2. Set up the equation
5 + 5x = 80
3. Solve for x
5 (-5) + 5x = 80 (-5)
5x = 75
5x (/5) = 75 (5)
x = 15
15
7) The angles are (x/2 + 4) and 46
1. Set up the equation
(x/2 + 4) + 46 = 180
2. Combine like terms
x/2 + (4 + 46) = 180
x/2 + 50 = 180
3. Solve for x
x/2 + 50 (-50) = 180 (-50)
x/2 = 130
Reciprocal
x/2 (*2) = 130 (*2)
x = 260
260
8) Angles are (3x - 1) and 160
1. subtract total angle measure from given
180 - 160 = 20
2. Set up equation
3x - 1 = 20
3. Combine like terms
No like terms move to step 4
4. Solve for x
3x - 1 (+1) = 20 (+1)
3x = 21
3x (/3) = 21 (/3)
x = 7
7
To make sure you got the questions right, substitute x with the answer you got.
I will not be doing so with all of them, but I will do it with one of them to show you.
Check work) #7
1. Set up original equation
(x/2 + 4) + 46 = 180
2. Substitute x with the value found earlier
x = 260
[(260)/2 + 4] + 46 = 180
3. Solve
[130 + 4] + 46 = 180
134 + 46 = 180
180 = 180
Answer is correct
I hope this helps, don't be afraid to reach out with any further and future questions!
