Questions: A quadrilateral has angles that measure 100°, 50°, 100°, and f. What is f? f=

To find the measure of the fourth angle \(f\) in a quadrilateral, we need to use the fact that the sum of the interior angles of a quadrilateral is always \(360^{\circ}\).

Given the angles of the quadrilateral are \(100^{\circ}, 50^{\circ}, 100^{\circ}\), and \(f\), we can set up the equation:

\[ 100^{\circ} + 50^{\circ} + 100^{\circ} + f = 360^{\circ} \]

First, add the known angles:

\[ 100^{\circ} + 50^{\circ} + 100^{\circ} = 250^{\circ} \]

Now, substitute this sum back into the equation:

\[ 250^{\circ} + f = 360^{\circ} \]

To find \(f\), subtract \(250^{\circ}\) from \(360^{\circ}\):

\[ f = 360^{\circ} - 250^{\circ} = 110^{\circ} \]

Therefore, the measure of the fourth angle \(f\) is \(110^{\circ}\).

\[ f = 110^{\circ} \]