Question

I need help with this please

Answer 1

Answer:

∠BIF = 126°

∠JBC = 63°

∠BJD = 117°

Step-by-step 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°