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.
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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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