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Rhombus JKLM is shown below. Find m∠KLM.

A.36°degree

B.38°degree

C,72°degree

D.76°degree

Rhombus JKLM is shown below. Find m∠KLM. A.36°degree B.38°degree C,72°degree D.76°degree-example-1
User Waldi
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1 Answer

3 votes

Answer:

Option D

Explanation:

Properties of a rhombus,

1). Diagonals of a rhombus bisect the opposite angles.

2). Sum of adjacent two angles of a rhombus is 180°.

By property (1),

Diagonal JL will bisect the angles ∠MJK and ∠KLM.

Therefore, m∠KLM = 2(5x + 3)°

Similarly, diagonal KM will bisect the angles ∠JKL and JML.

Therefore, m∠JKL = 2(9x - 11)°

By property (2),

2(9x - 11)° + 2(5x + 3)° = 180°

9x - 11 + 5x + 3 = 90

14x - 8 = 90

14x = 98

x = 7

Since, m∠KLM = 2(5x + 3)°

= 2(5×7 + 3)°

= 76°

Therefore, Option D will be the answer.

User Beshio
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