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A house built on a hill still needs to have vertical walls and floors in order to be stable. What value of x is needed in order for this house to be stable?
 

The problem involves calculating the value of \( x \) for which the house's vertical walls remain stable. From the image, two angles are marked as:

- \( (3x + 5)^\circ \) for the left side of the house
- \( (x + 15)^\circ \) for the right side of the house

Since the house's walls are vertical and the sum of these two angles must form a right angle (90°) when added, we can set up the equation as follows:

\[
(3x + 5) + (x + 15) = 90
\]

Now, simplify the equation:

\[
3x + 5 + x + 15 = 90
\]

\[
4x + 20 = 90
\]

Now, subtract 20 from both sides:

\[
4x = 70
\]

Finally, divide both sides by 4:

\[
x = \frac{70}{4} = 17.5
\]

It seems like the correct answer isn't among the choices, which suggests there may be an issue with the choices provided or the assumption of the problem. The nearest choice could be an approximation or rounding error in the options.

Would you like me to analyze the question further or explain the reasoning behind this?

A house built on a hill still needs to have vertical walls and floors in order to be stable. What value of x is needed in order for this house to be stable?

In this problem, you will calculate the value of x to ensure a house's walls are vertical and stable on a sloped surface. Using angle sums and solving a linear equation, this problem is perfect for students in Grades 7-9.

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