Question

BCDE is a rectangle, ZOCD = 47°. Find
angles x, y and z. If BD = 5a - 3 and EC =
a +5. Find a, length of EC.
С
B
у
47°
Z
Х
E
D​

Answer 1

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:

BCDE is rectangle

Diagonals of rectangle are equal in length and bisect each other

=> BD  = CE

=> 5a - 3 = a + 5

=> 4a = 8

=> a = 2

5a - 3 = 5(2) - 3 = 7

a + 5 = 2 + 5 = 7

Length of EC = 7

OD = OC

=> x = 47°

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

=> z  = 47°  +  47°

=>  z = 94°  

y =  x  ( alternate interior angle)

=>  y = 47°  

x = 47° ,    y = 47°    ,  z = 94°     ,  EC = 7

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