Question

BCDE is a rectangle, Z
/_OCD = 47° Find angles x, y and z. If BD = 5a - 3 and EC = a + 5. Find a, length of EC.

PLEASE ANSWER THE QUESTION IF YOU KNOW THE ANSWER IF YOUR ANSWER IS IRRILATIVE I'LL REPORT THAT ANSWER ​​
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Answer 1

Answer:

Step-by-step explanation:

For finding a,

We know that the diagonals of the rectangle are equal,

⇒ BD = CE

⇒ 5a - 3 = a + 5

⇒ 5a - a = 5 + 3

⇒ 4a = 8

⇒ a = 2

Length of EC = a + 5 = 2 + 5 = 7

  EC = 7

This image shows a solution to find x, y and z

Answer 2

Given : BCDE is a rectangle, ∠OCD = 47°

BD = 5a - 3 and EC = a + 5.

To Find : angles x, y and z.

Length of EC

Solution:

Diagonals of rectangle are equal and bisect each other,

BD = EC

=> 5a - 3 = a + 5

=> 4a = 8

=> a = 2

BD = 5(2) - 3 = 7

EC = 2 + 5 = 7

OC = OD  ( Diagonal equal and bisect )

=> x = 47°    ( Angles opposite to equal sides are equal )

z = x + 47°   ( exterior  angle = sum of opposite two interior angles )

=> z  = 47° + 47°  = 94°

y = x   ( alternate angle as BE || CD  , opposite sides of rectangle )

=> y = 47°

a = 2

BD  = 7

EC = 7

x = 47°

y = 47°

z= 94°

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