Question

name
date
find the value of each variable in the parallelogram.
1.
2.
3.
4.
5.
6.

Explanation:

Problem 1:

Step1: Recall parallelogram side property

In a parallelogram, opposite sides are equal. So the side opposite to length 8 is \( y \), and opposite to 11 is \( x \).
Thus, \( y = 8 \) and \( x = 11 \).

Step1: Apply side equality for parallelogram

Opposite sides of a parallelogram are equal. So, for the horizontal sides: \( a - 3 = 14 \), and for the vertical sides: \( b + 2 = 7 \).

Step2: Solve for \( a \)

From \( a - 3 = 14 \), add 3 to both sides: \( a = 14 + 3 = 17 \).

Step3: Solve for \( b \)

From \( b + 2 = 7 \), subtract 2 from both sides: \( b = 7 - 2 = 5 \).

Step1: Recall parallelogram angle property

In a parallelogram, consecutive angles are supplementary (sum to \( 180^\circ \)). Given one angle is \( 101^\circ \), so \( 101 + m = 180 \).

Step2: Solve for \( m \)

Subtract 101 from both sides: \( m = 180 - 101 = 79 \).

Answer:

\( x = 11 \), \( y = 8 \)

Problem 2: