The way to do it can be explained like this:
Say AB and CD are the two parallel lines cut by a transversal at E and F respectively.
Then the pairs of alternate interior angles are:
Angle(AEF) and Angle(DFE)
Angle(CFE) and Angle(BEF)
Now lets prove if this is true:
<span>Angle(CFE) +Angle(DFE) = 180
(linear pair)
Also
Angle(CFE) +Angle(AEF) = 180
(Corresponding angles)
</span><span>Equate the above results:
Angle(CFE) +Angle(DFE) = Angle(CFE) +Angle(AEF)
</span><span>Angle(DFE) = Angle(AEF)
</span>Happens the same with
<span>Angle(CFE) = Angle(BEF)
</span>Hope this is very useful for you
Answer:
x = 7
Step-by-step explanation:
A triangle's total interior angle measurement will equal 180°.
Set all measurements equal to 180:
(82) + (9x - 6) + (6x - 1) = 180
Simplify. Combine like terms:
(82 - 6 - 1) + (9x + 6x) = 180
(82 - 7) + (15x) = 180
(75) + 15x = 180
Next, isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operation, and stands for:
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
~
First, Subtract 75 from both sides of the equation:
15x + 75 = 180
15x + 75 (-75) = 180 (-75)
15x = 180 - 75
15x = 105
Next, divide 15 from both sides of the equation:
(15x)/15 = (105)/15
x = 105/15
x = 7
7 is your value for x.
~
Answer:
2500
Step-by-step explanation:
Let the first square number be 
then the next square number is 
.
The difference between these two consecutive numbers is 99.
This implies that:
We expand to get:
Simplify:
Divide both sides by 2
Therefore the value of the larger perfect number is
.
