A rhombus with vertices L, M, K, and F that looks like a diamond.

Question

If m∠MKA=18.5° , which two statements would need to be true if LMKF is a rhombus?

(1 point)
Responses

m∠KMA=18.5°m∠KMA=18.5°

m∠MKF=37°m∠MKF=37°

m∠LFA=71.5°m∠LFA=71.5°

m∠MLA=71.5°m∠MLA=71.5°

m∠MAK=18.5°

Answer 1

In a rhombus, opposite angles are equal and adjacent angles are supplementary (they add up to 180°).

If \( m∠MKA = 18.5° \), then the following statements must be true:

1. The opposite angle, \( m∠KMA \), must also be equal to \( 18.5° \) (since opposite angles in a rhombus are equal).

2. The adjacent angle, \( m∠MKF \), would be \( 180° - 18.5° = 161.5° \). Therefore, \( m∠LFA \) and \( m∠MLA \) would both equal \( 161.5° \) (again, due to the properties of the rhombus).

To answer your question, the two statements that would need to be true are:

1. \( m∠KMA = 18.5° \) (this reflects the property of opposite angles being equal).
2. \( m∠MKF + m∠MKA = 180° \), giving \( m∠MKF = 161.5° \) (not listed in your options).

Since I see that the options provided do not directly correspond to 161.5°, the only true statements among your options based on \( m∠MKA = 18.5° \) would be:

• \( m∠KMA=18.5° \)
• \( m∠LFA=71.5° \) would be a misunderstanding because \( LFA \) should actually equal 161.5°, the addition of the adjacent angles should be \( 180° \).

To clarify: \( m∠KMA=18.5° \) is correct. You may want to look for an option that mentions complementary angles summing to 180°.

So, your correct choice is:

• m∠KMA=18.5°

(Note: It looks like there is a confusion in one of your options regarding the sum of angles; make sure to validate adjacent angles having a total of 180° for a rhombus.)