Answer:
x= 13/3
y=7.5
AB is 97/3
ABC is 122
Step-by-step explanation:
A rhombus is a special type of quadrilateral that has 4 equal sides and perpendicular diagonals which bisect each other and the angles. Knowing this then 4x+15 is equal to 7x+2 and 12y is equal to 90. Solve for each variables then substitute as needed to find the remaining values.
4x+15=7x+2
15=3x+2
13=3x
13/3 = x
BC is 4x+15 = 4(13/3)+15 = 52/3 + 45/3 = 97/3
CD is 7x+2 = 7(13/3)+2 = 91/3 + 6/3 = 97/3
Now solve for 12y=90 and y = 7.5.
Angle AFB is 12(7.5) = 90
Angle BCF is 4y-1 = 4(7.5)-1 = 29
Since the diagonal bisects the angle this means angle BCD is 58. So angle ABC will be 180-58 = 122
