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Select ALL the correct answers.
Matt drew quadrilateral JKLM inscribed in a circle. Which statements could describe the angles in quadrilateral JKLM?
a. m∠L = 125°, m∠J = 35°, and m∠K = 65°
b. m∠M = 55°, m∠J = 48°, and m∠L = 132°
c. m∠J = 84°, m∠K = 12°, and m∠M = 78°
d. m∠L = 40°, m∠M = 60°, and m∠K = 120°
e. m∠K = 72°, m∠L = 44°, and m∠M = 108°
f. m∠J = 105°, m∠K = 65°, and m∠L = 75°

Respuesta :

MrRoyal

When a quadrilateral is inscribed in a circle, the opposite angles are supplementary

The description of the angles in the quadrilaterals are:

  • b. m∠M = 55°, m∠J = 48°, and m∠L = 132°
  • d. m∠L = 40°, m∠M = 60°, and m∠K = 120°
  • e. m∠K = 72°, m∠L = 44°, and m∠M = 108°
  • f. m∠J = 105°, m∠K = 65°, and m∠L = 75°

How to describe the angles

The quadrilateral is given as: JKLM

The opposite angles are:

  • Angles J and L
  • Angles K and M

The opposite angles are supplementary

So, we have:

[tex]J + L = 180[/tex]

[tex]K + M = 180[/tex]

Next, we test the options

Option (a)

[tex]J + L = 180[/tex]

[tex]125 + 35 = 160[/tex]

This is not true

Option (b)

[tex]J + L = 180[/tex]

[tex]48 + 132 =180[/tex]

This is true

Option (c)

[tex]K + M = 180[/tex]

[tex]12 + 78 = 180[/tex]

This is not true

Option (d)

[tex]K + M = 180[/tex]

[tex]120 + 60 = 180[/tex]

This is true

Option (e)

[tex]K + M = 180[/tex]

[tex]72 + 108= 180[/tex]

This is true

Option (f)

[tex]J + L = 180[/tex]

[tex]105 + 75 = 180[/tex]

This true

Hence, the description of the angles in the quadrilaterals are (b), (d), (e) and (f)

Read more about inscribed quadrilaterals at:

https://brainly.com/question/26690979

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