Answer:
[tex]y=42[/tex]
Skills needed: Rhombus Geometry
1) We need to understand a property of rhombi (plural of rhombus) that is important in this problem.
---> [tex]\overline{AC}[/tex] is a diagonal in the rhombus.
---> [tex]\overline{BD}[/tex] is also a diagonal in the rhombus.
- In a rhombus, the diagonals are always perpendicular to each other.
---> Let's make the point of intersection of the diagonals as Point E.
[tex]\angle BEC=90[/tex]
---> This angle is needed to solve the problem for y.
2) Using triangle properties:
---> The sum of interior angles of a triangle equal 180.
- Take [tex]\triangle{BEC[/tex], which has 3 angles:
[tex]\angle{BEC}, \angle{ECB}, \angle{CBE}[/tex]
[tex]\angle{BEC+\angle{ECB + \angle{CBE=180[/tex]
[tex]\angle{BEC=90[/tex] due to rhombus diagonal property
[tex]\angle{ECB=48[/tex] which is given
[tex]\angle{EBC=y[/tex] (what we are trying to solve for)
Let's plug in!
3) [tex]90+48+y=180 \\ 138+y=180 \\ y=42[/tex]
y equals 42
