Answer:
∠BIF = 126°
∠JBC = 63°
∠BJD = 117°
Explanation:
adjacent angles in a rhombus add up to 180°
∠IBJ and ∠BIF are adjacent angles in a rhombus
thus,
∠IBJ + ∠BIF = 180°
54° + ∠BIF = 180
subtract 54 from both sides to isolate the variable
∠BIF = 126°
a line is 180°
thus, ∠IBA + ∠IBJ + ∠JBC = 180° as those three angles form a line
as the parallelograms are congruent, and we can visually notice that ∠IBA corresponds to angle ∠JBC, we can say that ∠IBA = ∠JBC
thus,
∠IBA + ∠IBJ + ∠JBC = 180°
54° + ∠JBC + ∠JBC = 180°
54° + 2∠JBC = 180
subtract 54 from both sides to isolate the variable and its coefficient
126° = 2∠JBC
divide 2 from both sides to isolate the variable
∠JBC = 63°
adjacent angles in a parallelogram add up to 180°
∠JBC and ∠BJD are adjacent angles in a parallelogram
∠JBC + ∠BJD = 180°
63° + ∠BJD = 180°
subtract 63 from both sides to isolate the variable
∠BJD = 117°