The four angles of a pentagon is 40 degrees ,75 degrees ,125 degrees and 135 degrees .the measure of the fifth angle is ?
give the solution how its came
you recall that the sum of the interior angles of a pentagon is 540.
To find the measure of the fifth angle of the pentagon, you need to know the sum of the interior angles of a pentagon.
The formula to calculate the sum of the interior angles of a polygon is: (n-2) * 180 degrees, where n is the number of sides of the polygon.
For a pentagon (a polygon with 5 sides), the sum of the interior angles can be calculated as: (5-2) * 180 degrees = 3 * 180 degrees = 540 degrees.
Given that the four angles of the pentagon are 40 degrees, 75 degrees, 125 degrees, and 135 degrees, you can find the measure of the fifth angle by subtracting the sum of the four known angles from the sum of the interior angles.
Sum of the four known angles = 40 degrees + 75 degrees + 125 degrees + 135 degrees = 375 degrees.
Measure of the fifth angle = Sum of the interior angles - Sum of the four known angles = 540 degrees - 375 degrees = 165 degrees.
Therefore, the measure of the fifth angle of the pentagon is 165 degrees.
To find the measure of the fifth angle of the pentagon, we can start by finding the sum of the known angles.
Adding all the given angles: 40 + 75 + 125 + 135 = 375 degrees.
We know that the sum of the angles in a pentagon is 540 degrees. So, to find the measure of the fifth angle, we subtract the sum of the known angles from 540.
540 - 375 = 165 degrees.
Therefore, the measure of the fifth angle is 165 degrees.