If angle K measures 67° and angle L measures 119°, what are the measures of angles M and N in quadrilateral LMNK with circle O inscribed?

In a quadrilateral with an inscribed circle, the sum of the measures of the angles opposite each other must be equal. This means that:

• Angle K + Angle M = 180°
• Angle L + Angle N = 180°

Given:

• Angle K = 67°
• Angle L = 119°

To find Angle M:

Angle M = 180° – Angle K = 180° – 67° = 113°

To find Angle N:

Angle N = 180° – Angle L = 180° – 119° = 61°

Therefore, the measures of angles M and N are:

• Angle M = 113°
• Angle N = 61°