Answer:
[tex]x=5[/tex]
Step-by-step explanation:
The complete question is
m ∠ A = 100 - x
m ∠ B = 80 + x
m ∠ C = 110 - 3x
m ∠ D = 75 + 2x
Quadrilateral ABCD is a parallelogram if both pairs of opposite angles are equal. Prove that Quadrilateral ABCD is a parallelogram by finding the value of x.
Options
A) x = 5
B) x = 7
C) x = 10
D) x = 15/2
we know that
In a parallelogram, opposite angles are parallel and consecutive angles are supplementary
so
m ∠ A=m ∠ C
m ∠ B=m ∠ D
m ∠ A+m ∠ B=180°
m ∠ B+m ∠ C=180°
step 1
Find the value of x
we know that
m ∠ A=m ∠ C
substitute the given values
[tex](100-x)^o=(110-3x)^o[/tex]
solve for x
Group terms
[tex]3x-x=110-100[/tex]
Combine like terms
[tex]2x=10[/tex]
[tex]x=5[/tex]
step 2
Verify the measure of the angles
[tex]m\angle A=100-5=95^o[/tex]
[tex]m\angle B=80+5=85^o[/tex]
[tex]m\angle C=110-3(5)=95^o[/tex]
[tex]m\angle D=75+2(5)=85^o[/tex]
therefore
[tex]m\angle A=m\angle C[/tex] ---> is ok
[tex]m\angle B=m\angle D[/tex] ---> is ok
[tex]m\angle A+m\angle B=180^o[/tex] ---> is ok
[tex]m\angle B+m\angle C=180^o[/tex] ---> is ok
