To solve for the missing values, we need to use the properties of parallelograms:
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Consecutive angles are supplementary (their sum is 180 degrees).
Using property 3, we can solve for the missing angles:
For x = 2; ZANS 115°:
Let angle Z = a
Then angle A = 180 - 115 = 65 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 115 degrees
Angle S = 180 - 65 = 115 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 8; ZANS 70°:
Let angle Z = b
Then angle A = 180 - 70 = 110 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 70 degrees
Angle S = 180 - 110 = 70 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 2; ZANS 70°:
Let angle Z = c
Then angle A = 180 - 70 = 110 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 70 degrees
Angle S = 180 - 110 = 70 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 8; ZANS 115°:
Let angle Z = d
Then angle A = 180 - 115 = 65 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 115 degrees
Angle S = 180 - 65 = 115 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
Therefore, for all values of x, sides ZS and AN are parallel and congruent, and angles Z, A, N, and S have the values given above for each specific case.
Answers & Comments
Answer:
To solve for the missing values, we need to use the properties of parallelograms:
Opposite sides are parallel and congruent.
Opposite angles are congruent.
Consecutive angles are supplementary (their sum is 180 degrees).
Using property 3, we can solve for the missing angles:
For x = 2; ZANS 115°:
Let angle Z = a
Then angle A = 180 - 115 = 65 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 115 degrees
Angle S = 180 - 65 = 115 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 8; ZANS 70°:
Let angle Z = b
Then angle A = 180 - 70 = 110 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 70 degrees
Angle S = 180 - 110 = 70 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 2; ZANS 70°:
Let angle Z = c
Then angle A = 180 - 70 = 110 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 70 degrees
Angle S = 180 - 110 = 70 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
For x = 8; ZANS 115°:
Let angle Z = d
Then angle A = 180 - 115 = 65 degrees (consecutive angles are supplementary)
Opposite angles are congruent, so angle N = 115 degrees
Angle S = 180 - 65 = 115 degrees (consecutive angles are supplementary)
Using property 1, sides ZS and AN are parallel and congruent.
Therefore, for all values of x, sides ZS and AN are parallel and congruent, and angles Z, A, N, and S have the values given above for each specific case.