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Answer:
The value of x is 108°
Step-by-step explanation:
Given interior angles of parallelogram are:
<u>The sum of interior angles of a parallelogram is 360°.</u>
We will use this information to find the value of x.
So adding up all the angles and putting the sum equal to 360 we get,
Taking LCM on left side of the equation, as it involves fraction
Multiplying both sides by 3
Dividing both sides by 10
Hence,
The value of x is 108°
ANSWER
The general solution is , where
is an integer
<u>EXPLANATION</u>
In order to solve the linear congruence;
We need to determine the inverse of (which is a Bézout coefficient for 33).
To do that we must first use the Euclidean Algorithm to verify the existence of the inverse by showing that;
Now, here we go;
The greatest common divisor is the last remainder before the remainder of zero.
Hence, the .
We now express this gcd of 1 as a linear combination of 33 and 280.
We can achieve this by making all the non zero remainders the subject and making a backward substitution.
Equation (2) in equation (1) gives,
The above linear combination tells us that is the inverse of
.
Now we multiply both sides of our congruence relation by .
This implies that;
.
Since this is modulo, the solution is not unique because any integral addition or subtraction of the modulo (280 in this case) produces an equivalent solution.
Therefore the general solution is,
, where
is an integer