Question

Angle K measures 67º and angle L measures 119°.

Circle O is inscribed by quadrilateral L M N K.

What are the measures of angles M and N?

m Angle M = 61o and m Angle N = 113o
m Angle M = 67o and m Angle N = 119o
m Angle M = 113o and m Angle N = 61o
m Angle M = 119o and m Angle N = 67o

Answer 1

If the quadrilateral is inscribed in circle O, opposite angles are supplementary. So

- m∠M = 180° − m∠K = 180° − 67° = 113°
- m∠N = 180° − m∠L = 180° − 119° = 61°

Answer: m∠M = 113° and m∠N = 61°.