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Answer: The answer is 147° and 33°.
Step-by-step explanation: We are given a figure in which the line DE is parallel to the line FG and AG is a tranversal. We are to find the value of 'x' and 'y' from the figure.
Also, given that
∠ABE = (5y - 18)°.
We can see from the figure that ∠DBG and ∠ABE are vertically opposite angles, so they must be equal.
That is,
Also, since ∠DBG and ∠FGB are interior angles on the same side of the transversal, so their sum is 180°.
That is
Adding equations (i) and (ii), we get
and from equation (ii), we get
Thus, x° = 147° and y° = 33°.