Question

In rhombus FGHJ, m∠1=37°.

What is m∠2?

Answer 1

m∠2 = 53*

Explanation:

Answer 2

m∠2 = 53°

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 =
`(106)/(2)` = 53°

Therefore, m∠2 = 53°.