Question

given that wrst is a parallelogram, find the value of x or y in each question.

1. rs = 2x + 7, tw = 25, wr = 16
2. wz = 4x - 3, zs = 13
3. rz = 17, zt = 7y + 3
4. m∠wrs = 24x, m∠stw = 15x + 27
5. m∠wrs = 75, m∠rst = 7x

Explanation:

6.

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, $RS = TW$.
$2x + 7=25$

Step2: Solve for x

Subtract 7 from both sides: $2x=25 - 7=18$.
Then divide both sides by 2: $x=\frac{18}{2}=9$.

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $WZ = ZS$.
$4x−3 = 13$

Step2: Solve for x

Add 3 to both sides: $4x=13 + 3=16$.
Then divide both sides by 4: $x=\frac{16}{4}=4$.

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $RZ = ZT$.
$17=7y + 3$

Step2: Solve for y

Subtract 3 from both sides: $7y=17 - 3 = 14$.
Then divide both sides by 7: $y=\frac{14}{7}=2$.

Answer:

$x = 9$

7.