The values of x and y are ⇒ x = 4 and y = 9
Step-by-step explanation:
In a parallelogram
1. Each two opposite sides are equal and parallel
2. Each two opposite angles are equal
3. Its two diagonals bisect each other
In parallelogram ABCD
∵ Its diagonal AC and BD intersect each other at point E
∵ AC and DE bisect each other at E
∴ E is the mid-point of AC
∴ AE = EC
∴ E is the mid-point of BD
∴ DE = EB
∵ AE = x + 5
∵ EC = y
∵ AE = EC
∴ x + 5 = y ⇒ (1)
∵ DE = 2x + 3
∵ EB = y + 2
∵ DE = EB
∴ 2x + 3 = y + 2
- Subtract 2 from both sides
∴ 2x + 1 = y ⇒ (2)
Substitute y in equation (2) by equation (1)
∵ 2x + 1 = x + 5
- Subtract x from both sides
∴ x + 1 = 5
- Subtract 1 from both sides
∴ x = 4
Substitute the value of x in equation (1) to find y
∵ x + 5 = y
∵ x = 4
∴ 4 + 5 = y
∴ y = 9
The values of x and y are ⇒ x = 4 and y = 9
Learn more:
You can learn more about parallelograms in brainly.com/question/6779145
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