Question

Algebra Find the values for x and y in parallelogram ABCD. AE= x+5, EC=y, DE=2x+3, EB=y+2

Answer 1

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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