Answer:
21
Step-by-step explanation:
It is given that two lines are parallel, and hence the corresponding angles are congruent, by corresponding angles postulate. It is also given that the triangles in the photo share an angle, by the reflexive property, the shared angle is congruent. Hence one can use angle-angle to determine that the two triangles in the picture are similar.
Using this, one can set up a proportion with the sides. The ratios of any two corresponding sides are the same as any other two corresponding sides in the triangle, respectively, this is due to the corresponding parts of similar triangles theorem.
[tex]\frac{9+12}{12}=\frac{49}{49-?}[/tex]
Simplify,
[tex]\frac{21}{12}=\frac{49}{49-?}\\\\\frac{7}{4}=\frac{49}{49-x}[/tex]
Cross products,
[tex](7)(49-?) = (4)(49)\\\\343-7?=196[/tex]
Inverse operations,
[tex]343-7?=196\\-343\\\\-7? = -147\\/-7\\\\?=21[/tex]
