Answer: x = 8
Step-by-step explanation: The question shows two separate trapeziums DEFG and QRSP. In figure DEFG two sides and three angles are given. However, if we turn figure QRSP upside down, we can see that what we have is two similar trapeziums, DEFG and SPQR. Upon closer examination, we would see that line DE = line SP
Similarly line GF = line RQ
Also angle F = angle Q.
Having take note of these similarities, we can now express them as follows;
2x - 4 = 12 {i.e RQ = GF}
6y + x = 68 {i.e Q = F}
What we now have is a pair of simultaneous equations
2x - 4 = 12 ————(1)
6y + x =68 ————(2)
From equation (2)
x = 68 - 6y (by rearranging and making x the subject of the formula)
We can now substitute for the value of x into equation (1)
2x - 4 = 12
2(68 - 6y) - 4 = 12
By expanding the bracket, we now have
136 - 12y - 4 = 12
By regrouping and collecting like terms,
136 - 4 - 12 = 12y
Remember that if a negative number crosses to the other side of the equality sign, it becomes positive, and vice versa. Hence, negative 12y crosses to the right hand side of the equation and becomes positive 12y.
136 - 4 - 12 = 12y
120 = 12y
Divide both sides of the equation by 12
10 = y
Now we can substitute for the value of y = 10 into equation (2)
6y + x = 68
6(10) + x = 68
60 + x =68
Subtract 60 from both sides of the equation
x = 8.