4 interior angles of a pentagon are 90-a, 90+a, 110-2a, 110+2a. Find the fifth interior angle
sum of pentagon's angles is 540.
To find the fifth interior angle of the pentagon, we first need to know that the sum of all interior angles of a pentagon is always equal to 540 degrees.
Let's add up the given angles and equate it to the sum of the interior angles of a pentagon:
(90 - a) + (90 + a) + (110 - 2a) + (110 + 2a) + x = 540
Simplifying the left side of the equation gives us:
90 + 90 + 110 + 110 - (a + a) + (2a + 2a) + x = 540
380 + x = 540
Now, solve the equation for x:
x = 540 - 380
x = 160
Therefore, the fifth interior angle of the pentagon is 160 degrees.