The sum of the interior angles of a pentagon is equal to 540°. Given the following pentagon. Write and solve an equation in order to determine X.
Here are the numbers:
106°
94°
135°
x°
(x + 5)°
Show all work
(This is 10th grade math, please don't make it advanced)
To find the sum of the interior angles of a pentagon, we use the formula:
S = (n-2) * 180
where S is the sum of the interior angles and n is the number of sides (in this case, n = 5). So we have:
S = (5-2) * 180
S = 540°
Now we can use this information to set up an equation involving x:
106° + 94° + 135° + x° + (x + 5)° = 540°
Simplifying, we can combine like terms:
340° + 2x° + 5° = 540°
Subtracting 345° from both sides:
2x° = 195°
Dividing by 2:
x° = 97.5°
So the value of x is 97.5°.
To determine the value of X in the given pentagon, we can use the fact that the sum of the interior angles of a pentagon is equal to 540°.
Step 1: Write the equation:
106° + 94° + 135° + x° + (x + 5)° = 540°
Step 2: Simplify the equation:
106° + 94° + 135° + 2x + 5° = 540°
Step 3: Combine like terms:
335° + 2x + 5° = 540°
Step 4: Simplify further:
340° + 2x = 540°
Step 5: Subtract 340° from both sides to isolate the variable term:
2x = 540° - 340°
2x = 200°
Step 6: Divide both sides by 2 to solve for x:
x = 200° / 2
x = 100°
So, the value of X is 100°.