Two angles of a quadrilateral measure \( 194^{\circ} \) and \( 98^{\circ} \). The other two angles are in a ratio of \( 5: 12 \). What are the measures of those two angles? Submit

To find the measures of the other two angles in the quadrilateral, we first note that the sum of the interior angles of a quadrilateral is \( 360^{\circ} \). Given that two angles measure \( 194^{\circ} \) and \( 98^{\circ} \), we can calculate the sum of these two angles: \[ 194^{\circ} + 98^{\circ} = 292^{\circ} \] Now, we can find the sum of the remaining two angles: \[ 360^{\circ} - 292^{\circ} = 68^{\circ} \] Let the two remaining angles be \( 5x \) and \( 12x \) according to the given ratio of \( 5:12 \). The sum of these two angles is: \[ 5x + 12x = 17x \] Therefore, we can set up the equation: \[ 17x = 68^{\circ} \] Solving for \( x \): \[ x = \frac{68^{\circ}}{17} = 4^{\circ} \] Now we can find the measures of the two angles: \[ 5x = 5 \times 4^{\circ} = 20^{\circ} \] \[ 12x = 12 \times 4^{\circ} = 48^{\circ} \] Thus, the measures of the other two angles are \( \boxed{20^{\circ}} \) and \( \boxed{48^{\circ}} \).