Angle K measures 67º and angle L measures 119°. Circle O is inscribed by quadrilateral LMNK. What are the measures of angles M and N?

Solution:

Given, angle K = 67°

Angle L = 119°

Circle O is inscribed by quadrilateral LMNK

We have to find the measures of angles M and N.

Since it is a cyclic quadrilateral,

Angle K + Angle M = 180°

67° + Angle M = 180°

Angle M = 180° - 67°

Angle M = 113°

Similarly, Angle L + Angle N = 180°

119° + Angle N = 180°

Angle N = 180° - 119°

Angle N = 61°

Therefore, the measures of angles M and N are 113° and 61° respectively.

Angle K measures 67º and angle L measures 119°. Circle O is inscribed by quadrilateral LMNK. What are the measures of angles M and N?

Summary:

Angle K measures 67º and angle L measures 119°. Circle O is inscribed by quadrilateral LMNK. The measures of angles M and N are 113° and 61° respectively.