Question

HELP ASAP!!!!!!!!PLEASE Solve for x. Please explain. Thank you

Answer 1

The values are $x=8$ and $y=10$

Explanation:

From the figure, we can see that the two quadrilaterals are similar.

Thus, by the property of quadrilateral, for similar quadrilaterals, their corresponding angles and sides are congruent. Thus, we have,

∠D = ∠S, ∠E = ∠P, ∠G = ∠R and ∠F = ∠Q

Also, GF = QR and DE = PS

Where QR = $2x-4$ and ∠D = 102°, ∠G = 84° and ∠F = 68°, ∠Q = $(6y+x)$°

Hence, to determine the value of x for the side QR, we have,

Equating the values in GF = QR,we get,

$12=2x-4\\16=2x\\8=x$

Thus, the value of x is 8.

Substituting x in the angle Q to determine the value of y.

Thus, we have,

∠F = ∠Q

$68=6y+x\\68=6y+8\\60=6y\\10=y$

Thus, the value of y is 10.

Hence, The values are $x=8$ and $y=10$