in a pentagon each of the two angles measuer 76 degrees another angle measueres 111 degrees and the fourth measures 146 degrees. what is the measuer of the missing angle?
what is it can you explain step by step please!
The sum of the angles = 360.
Add up 76 + 76 + 111 + 146 and subtract that sum from 360
but if you add those together you get 409
To find the measure of the missing angle in a pentagon, we can start by using the fact that the sum of the interior angles of a polygon with n sides is given by the formula: (n - 2) * 180 degrees.
In this case, we have a pentagon, which has 5 sides. So, using the formula, we can calculate the sum of the interior angles: (5 - 2) * 180 = 3 * 180 = 540 degrees.
Now, we know the measurements of four angles in the pentagon: 76 degrees, 76 degrees, 111 degrees, and 146 degrees. We can add them together to find the sum of these four angles: 76 + 76 + 111 + 146 = 409 degrees.
To find the measure of the missing angle, we need to subtract the sum of the four known angles from the sum of the interior angles of the pentagon. Hence, 540 - 409 = 131 degrees.
Therefore, the missing angle in the pentagon measures 131 degrees.