If m∠MKA=18.5°

𝑚

𝑀
𝐾
𝐴
=
18.5
°
, which two statements would need to be true if LMKF
𝐿
𝑀
𝐾
𝐹
is a rhombus?

(1 point)
Responses

m∠LFA=71.5°
𝑚

𝐿
𝐹
𝐴
=
71.5
°
m∠LFA=71.5°
𝑚

𝐿
𝐹
𝐴
=
71.5
°

m∠MLA=71.5°
𝑚

𝑀
𝐿
𝐴
=
71.5
°
m∠MLA=71.5°
𝑚

𝑀
𝐿
𝐴
=
71.5
°

m∠KMA=18.5°
𝑚

𝐾
𝑀
𝐴
=
18.5
°
m∠KMA=18.5°
𝑚

𝐾
𝑀
𝐴
=
18.5
°

m∠MAK=18.5°
𝑚

𝑀
𝐴
𝐾
=
18.5
°
m∠MAK=18.5°
𝑚

𝑀
𝐴
𝐾
=
18.5
°

m∠MKF=37°

1 answer

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

Given that \( m∠MKA = 18.5° \), we can determine the following:

  1. The opposite angle \( m∠KMF \) is also \( 18.5° \) because opposite angles in a rhombus are equal.
  2. The adjacent angle \( m∠LKA \) would be \( 180° - 18.5° = 161.5° \).
  3. Therefore, the other angles must also be equal to their opposite angles.

To find which statements should be true if \( LMKF \) is a rhombus, we look for relationships tied to these properties.

  • Since \( m∠MKA = 18.5° \), the adjacent angles could be \( m∠MLA \) or \( m∠LFA \).
  • For \( m∠MKA = 18.5° \):
    • The consecutive angles should be \( m∠LFA = 180° - 18.5° = 161.5° \) or \( m∠MLA = 161.5° \).

Among the choices provided, we are looking for a pair of statements that work with \( 18.5° \).

  1. Option: \( m∠LFA = 71.5° \) is incorrect because \( 71.5° \) doesn't equal \( 161.5° \).
  2. Option: \( m∠MLA = 71.5° \) is incorrect for the same reason.
  3. Option: \( m∠KMA = 18.5° \) is true because it reflects symmetry.
  4. Option: \( m∠MAK = 18.5° \) is true due to the same symmetry in angles, but this does not characteristically help make conclusions about other angles.
  5. Option: \( m∠MKF = 37° \) is not directly relevant to the conditions of a rhombus as described.

Thus, the two statements that must be true if \( LMKF \) is a rhombus are "m∠KMA = 18.5°" and "m∠MAK = 18.5°". These reflect the requirement for equal opposite angles in the rhombus.