Answer:
x = 10
y = 5
Step-by-step explanation:
Since, two lines p and q are the parallel lines and FA is a transversal line intersecting these parallel lines.
ΔAOB and ΔDOC are the similar triangles.
Therefore, by the property of similar triangles, corresponding sides of the similar triangles will be proportional.
[tex]\frac{AO}{OD}= \frac{OB}{OC}[/tex]
[tex]\frac{x}{15}= \frac{8}{12}[/tex]
x = [tex]\frac{15\times 8}{12}[/tex]
x = 10
Similarly, triangles AOB and OEF will be similar.
And by the property of similar triangles,
[tex]\frac{AO}{OF}= \frac{OB}{OE}[/tex]
[tex]\frac{x}{15+y}= \frac{8}{12+4}[/tex]
[tex]\frac{10}{15+y}= \frac{8}{16}[/tex]
8(15 + y) = 160
120 + 8y = 160
8y = 160 - 120
8y = 40
y = 5
