Answer:
n=5
x= 23
p= 4
Step-by-step explanation:
What this wants us to do is find the value of the variable first, then find the measurement of the degrees.
So, for the first equation we need to make an equation.
Since the angles are vertical angles, that means they equal each other.
The equation would be.. 8n=9n-5.
Step 1- Move variable to the left hand side and change its sign
8n-9n= -5
Step 2- Collect like terms
-n= -5
Step 3- Change signs on both sides of the equation
n=5
So, now that we know what the variable is, substitute it into the equations.
8(5)= 40 9(5)-5= 40
For the second equation, the angles equal 180 degrees.
So, that would give us the equation.. 6x+19+x= 180.
Step 1- Add the common variables
(6x+x)+19= 180
7x+19= 180
Step 2- Subtract 19 from both sides.
7x+19= 180
-19 -19
7x= 161
Step 3- Divide both sides by 7
<u>7x</u>= <u>161</u>
7 7
x= 23
So, now that we know what the variable is, substitute it into the equations.
6(23)+19= 157
157+23= 180
Finally for the last equation, they are vertical angles, so they equal each other.
So, the equation would be 5p+28= 12p.
Step 1- Move the variable to on side.
5p+28= 12p
-5p -5p
28= 12-5p
Step 2- Subtract the variables
28= 7p
Step 3- Divide by 7 to both sides.
<u>28</u>= <u>7p</u>
7 7
p= 4
So, now that we know what the variable is, substitute it into the equations.
5(4)+28= 48
12(4)= 48
Hope this helps!! :)
