In a pentagon, the sum of interior angles is 540 degrees. Given angles 148, 112, 90, x, and 3x + 10, solving for x yields x = 45 degrees. This satisfies the conditions, ensuring the sum of angles in the pentagon remains consistent with the polygon's interior angle formula.
In a pentagon, the sum of all interior angles is given by the formula 180(n-2) degrees, where n is the number of sides. For a pentagon, n = 5, so the sum is 180(5-2) = 540 degrees. Each angle contributes to this sum.
The given angles in the pentagon are 148, 112, 90, x, and 3x + 10. Adding these angles together, we get the equation:
148 + 112 + 90 + x + (3x + 10) = 540.
Combine like terms:
360 + 4x = 540.
Subtract 360 from both sides:
4x = 180.
Divide by 4:
x = 45.
So, the value of x is 45 degrees.
In conclusion, by applying the formula for the sum of interior angles in a polygon and equating it to the sum of the given angles in the pentagon, we find that x = 45 degrees. This satisfies the conditions for the angles in the pentagon, ensuring the total sum is 540 degrees.