Three angles of a quadrilateral are 72 and 105 . What is the exterior angle of the fourth angle ?
The sum of the angles in a quadrilateral is 360 degrees. We are given two angles: 72 and 105.
360 - 72 - 105 = 183
So the total of the third and fourth angles is 183 degrees.
Since the exterior angle of a polygon is equal to the sum of its interior angles, we can subtract 183 from 360 to find the exterior angle of the fourth angle:
360 - 183 = 177
Therefore, the exterior angle of the fourth angle is 177 degrees.
To find the exterior angle of the fourth angle in a quadrilateral, you can use the fact that the sum of the interior angles of a quadrilateral is 360 degrees.
Let's denote the fourth angle as x.
The sum of the interior angles of a quadrilateral is given by the formula:
Sum of Interior Angles = (n - 2) * 180, where n is the number of sides of the polygon.
Since a quadrilateral has four sides, the sum of its interior angles is:
360 = (4 - 2) * 180
Simplifying this equation gives:
360 = 2 * 180
So, we know that the sum of the interior angles of the quadrilateral is 360 degrees.
Now, we can find the sum of the given angles 72 and 105:
72 + 105 = 177
To find the measure of the fourth angle, we can subtract the sum of the given angles from the sum of the interior angles:
x = 360 - 177
x = 183
Therefore, the measure of the exterior angle of the fourth angle is 183 degrees.