A quadrilateral has two angles that measure \( 247^{\circ} \) and \( 51^{\circ} \). The other two angles are in a ratio of \( 11: 20 \). What are the measures of those two angles? \( \square^{\circ} \) and

The sum of the angles in any quadrilateral is always \( 360^{\circ} \). Here, we add the given angles: \( 247^{\circ} + 51^{\circ} = 298^{\circ} \). Now, subtract this from \( 360^{\circ} \) to find the sum of the other two angles: \( 360^{\circ} - 298^{\circ} = 62^{\circ} \). Let the measures of the two unknown angles be \( 11x \) and \( 20x \) based on the given ratio. The equation is \( 11x + 20x = 62^{\circ} \), which simplifies to \( 31x = 62^{\circ} \). Solving for \( x \) gives \( x = 2 \). Thus, the angles are \( 11x = 22^{\circ} \) and \( 20x = 40^{\circ} \). The measures of the two angles are \( 22^{\circ} \) and \( 40^{\circ} \).