The sum of the interior angles of a quadrilateral is always 360 degrees. Therefore, we can find the value of the third interior angle by subtracting the sum of the given angles from 360:
360 - (125 + 72) = 360 - 197 = 163 degrees
So, the third interior angle is 163 degrees.
The sum of an interior angle and its corresponding exterior angle is always 180 degrees. Since the given exterior angle is 116 degrees, we can find the value of the corresponding interior angle by subtracting it from 180:
180 - 116 = 64 degrees
Now, let's label the fourth interior angle as y. We know that the sum of the interior angles is 360 degrees, so we can set up the equation:
125 + 72 + 163 + y = 360
Simplifying, we have:
360 + y = 360
Subtracting 360 from both sides, we get:
y = 0
Therefore, the value of y is 0.
Now, let's label the remaining exterior angle as x. By the same reasoning as before, we can find the corresponding interior angle:
180 - x = 72 (since the given interior angle is 72)
Simplifying, we have:
180 - 72 = x
x = 108
Therefore, the value of x is 108.
If two interior angles of a quadrilateral are 125 degrees and 72 degrees and an exterior angle is 116, what is the value of x and y?
1 answer
1 answer