Question

problem 5 determine the measure of the missing angle.

Explanation:

Step1: Recall angle - sum property of a quadrilateral

The sum of the interior angles of a quadrilateral is $360^{\circ}$.

Step2: Identify known angles

We know that one angle is $90^{\circ}$ (the right - angle), another is $128^{\circ}$ and the third is $28^{\circ}$. Let the missing angle be $x$.
So, $x + 90^{\circ}+128^{\circ}+28^{\circ}=360^{\circ}$.

Step3: Solve for the missing angle

First, add the known angles: $90 + 128+28=246^{\circ}$.
Then, $x=360^{\circ}-246^{\circ}$.
$x = 114^{\circ}$.

Answer:

$114^{\circ}$