Final answer:
To find the values of x and y in the quadrilateral, we use the sum of interior angles property (360 degrees) and the supplementary nature of interior and exterior angles (180 degrees). Solving the resulting equations, we determine that x = 99 degrees and y = 64 degrees.
Step-by-step explanation:
To determine the values of x and y in a quadrilateral given two interior angles and one exterior angle, we need to recall two important properties of polygons:
- The sum of the interior angles in a quadrilateral is 360 degrees.
- The exterior angle of a polygon is supplementary to its adjacent interior angle (meaning they add up to 180 degrees).
Here, we have interior angles of 125 degrees and 72 degrees. Let's denote the other two unknown interior angles as x and y. Considering that their sum with the known angles should be 360 degrees, we can form the equation:
125 + 72 + x + y = 360
Simplifying this equation, we find:
x + y = 163 degrees
Regarding the exterior angle of 116 degrees, it is supplementary to the interior angle adjacent to it, let's say y. Hence, we have:
116 + y = 180 degrees
Slightly simplifying gives us:
y = 64 degrees
Substituting the value of y into the first equation, we have:
x + 64 = 163
Finally, solving for x provides:
x = 99 degrees
Thus, the values we find are x = 99 degrees and y = 64 degrees.