Question

Select ALL the correct answers.

Answer 1

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:

$J + L = 180$

$K + M = 180$

Next, we test the options

Option (a)

$J + L = 180$

$125 + 35 = 160$

This is not true

Option (b)

$J + L = 180$

$48 + 132 =180$

This is true

Option (c)

$K + M = 180$

$12 + 78 = 180$

This is not true

Option (d)

$K + M = 180$

$120 + 60 = 180$

This is true

Option (e)

$K + M = 180$

$72 + 108= 180$

This is true

Option (f)

$J + L = 180$

$105 + 75 = 180$

This true

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

Read more about inscribed quadrilaterals at:

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