The shape shown above is a pentagon. The sum of all angles inside a pentagon should always be equal to 540 degrees.
So, the first step is to find the easy angles.
The first one is the one on top that says 110.
180 is a straight line, so 180 - 110 is 70.
So that angle on top is 70.
So far, we have two angles.
70 and 110.
So, let's subtract that from what the pentagon should be.
540 - 70 - 110 = 360
So, the angles we have left should equal 360.
The first angle we should make a algebraic equation for is 2x.
Since we need the interior angle, that angle is actually 180 - (2x).
The next one is the one for x + 20, but we still need the interior angle.
So, this one is actually 180 - (x + 20).
Finally, the angle with x, we also need the interior angle so the algebraic equation for that angle is 180 - (x).
When you add 180 - (2x) , 180 - (x + 20) , and 180 - (x), you get
-4x + 520.
Now, we must make that equal to 360.
-4x + 520 = 360
-4x = -160
x = -160/-4
x = 40
Therefore, the value of x in this pentagon is 40 degrees.
