Question

statue a company is making different size statues that are in the shape of hour glasses. use the figure to find the missing measure, x°. the figure is not drawn to scale.

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°. In the two triangles formed in the hour - glass shape, the vertical angles are equal. Let the vertical angles be \(y\).

Step2: Consider the top triangle

In the top triangle, we know one angle is 64° and in the bottom triangle one angle is 70°. Since the vertical angles are equal, for the top triangle, if we let the third angle be \(x\), and using the angle - sum property of a triangle \(64^{\circ}+x + y=180^{\circ}\), and for the bottom triangle \(70^{\circ}+y + z = 180^{\circ}\), but \(y\) is the same in both. So, \(64 + x=70+z\). Also, since the vertical angles are equal, we can directly equate the sums of non - vertical angles of the two triangles. So \(64 + x=70\).

Step3: Solve for \(x\)

Subtract 64 from both sides of the equation \(64 + x=70\). We get \(x=70 - 64\).
\(x = 6\)

Answer:

6