The measure of an interior angle of a regular pentagon is 108 degrees.
Decide whether the statement is true or false. If false, provide a counterexample.
1. The equation 2x - 7 = 5 + x has exactly one solution TRUE
2. If x^2 = 16, then x must equal 8 or -8 TRUE
3. February 14 is Valentine's Day TRUE
4. If you visisted the Statue of Liberty, then you've been to New York TRUE
5. A point may lie on at most two lines FALSE A point may lie on more than zero to an infinite number of lines.
Write the converse and contropositive of each statement.
6. If you like tennis, then you play on the tennis team FALSE You don't have to. Haha.
7. If x is odd, then 2x is even TRUE
8. If m
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Answer:
The value of x = 5 and y =2
Step-by-step explanation:
Given: In parallelogram DEFG
DH = x+1 , HF= 3y , GH =3x-4 and HE = 5y+1.
In a parallelogram DEFG as shown below in the figure,
let H be the midpoint of parallelogram where the diagonals DF and GE of a parallelogram bisect each other.
then,by definition of parallelogram;
DH = HF and
GH=HE
Since, DH =HF
Substitute the given values above we get;
x+1 = 3y
or
x-3y = -1 ......[1]
and
GH = HE
3x-4 = 5y+1
or
3x - 5y = 5 ......[2]
On solving equation [1] and [2] simultaneously we get;
y =2
Substitute the value of y=2 in [1] we have;
x -3(2) = -1 or
x-6 = -1
Add 6 to both sides of an equation:
x-6+6 = -1+6
Simplify:
x = 5
Therefore, the values of x and y is; 5 and 2