Question

In the figure, ABCD is a square with BE = BF, AB = (7t - 6)cm and AD = (2t+9)cm. Find:
(a) the value of t
(b) the length of AB
(c) the angles x and y​

Answer 1

Answer:

T = 3

The length of AB is 15 cm

Angle x = 67.5 and angle y = 22.5

Step-by-step explanation:

7t - 6 = 2t + 9 which gives t =3

Put the value of t in 7t - 6

= 7(3) - 6

=21 - 6

=15

angle a = angle b = angle c = angle d = 90

Therefore: angle FBE = angle FCE = 45

angle x = angle BFE

angle CFE = 180 - BFE = 180 - x

Now using Angle sum property

y + 180-x + 45 = 180

=> x-y = 45 --------------------------------------------- eq. 1

Also, x + angle BFE(x) + 45 = 180

=> 2x = 135

x = 67.5

Now put the value of x in eq. 1

=> 67.5 - y = 45

= 67.5 - 45 = y

=> y = 22.5

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