Question

In rhombus FGHJ, m∠1=37°. What is m∠2?

Answer 1

Answer:

m∠2 = 53*

Step-by-step explanation:

Answer 2

Answer:

m∠2 = 53°

Step-by-step explanation:

We will use two properties of a rhombus to solve this problem.

1). Opposite angles of a rhombus are equal.

2). Diagonals bisect the angles.

Since ∠JFG and ∠JHG are the opposite angles of the rhombus,

m∠JFG = m∠JHG

Since, diagonal FH bisect ∠JHG,

m∠FHJ = m∠GHF = m∠JFH = m∠GFH = 37°

In triangle JFH,

m∠FHJ + m∠JFH + m∠HJF = 180°

37° + 37° + m∠HJF = 180°

m∠HJF = 180 - 74

            = 106°

Since, diagonal GJ bisects angle HJF,

m∠FJG = $\frac{106}{2}$ = 53°

Therefore, m∠2 = 53°.