Question

ABCD is a parallelogram. Find the value of x.

Answer 1

Opposite angles are equal in magnitude in parallelogram.

So, B+D = 360 - 2*118

B+D =360-236

B+D =124

5x-2 + 7x+4 = 124

12x+2 = 124

12x = 122

x = 122/12

x = 10.16

Answer 2

My answer would be as follows:

A = C and B = D
A = C = 118
B = D = 180 - 118 = 62

We draw a diagonal in the parallelogram which will cut the parallelogram into two triangles with angles 31-118-31. We can use the law of sines for this. We do as follows:

(7x+4) / sin 31 = y/sin 31
(5x-2) /sin 31 = y/sin 31

By substituation,

7x+4/ sin31 = 5x-2/sin 31
x = -3