Answer:
Given: It is given that and .
To Prove: ABCD is a parallelogram.
Statements
1. and
Reason: Given
2. are alternate interior angles
Reason: Def of alternate interior angles
3.
Reason: Alternate interior angles are congruent
4.
Reason: Reflexive property
5.
Reason: SAS congruency theorem
6.
Reason: Corresponding Parts of Congruent triangles are Congruent (CPCTC)
7. ABCD is a parallelogram
Reason: Parallelogram Side Theorem
Step-by-step explanation:
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The value of x in the parallelogram is 7.
In a parallelogram, it should be noted that the opposite angles are of equal measure.
In this case, 5x + 3 = 38
Collect like terms
5x = 38 - 3
5x = 35
x = 35/3
x = 7
In conclusion, x is 7.
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