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. the measure of the

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So the non - labeled angle in the left triangle and the non - labeled angle in the right triangle are equal. Let's call this common angle \( y\).

Step2: Apply the triangle angle - sum property

In a triangle, the sum of interior angles is \(180^{\circ}\).
For the left triangle: \(y + 68^{\circ}+ \text{(third angle)}=180^{\circ}\).
For the right triangle: \(y+66^{\circ}+x = 180^{\circ}\).
Since the two triangles have equal vertical angles (\(y\)), we can set up the equation based on the angle - sum property of triangles.
We know that \(68^{\circ}+\text{(left - triangle's third angle)}=66^{\circ}+x\) (because \(y\) is common).
Another way: Since the two triangles have vertical angles (equal), we use \(180 - 68=112\) (sum of the other two angles in the left triangle) and \(180-(66 + x)\) (sum of the other two angles in the right triangle). But using the direct angle - sum for each triangle:
For the left triangle (assuming the vertical angles are equal), if we consider the two triangles. Let the vertical angles be \(A\) (they are equal).
In the left triangle: \(A + 68+\text{(angle1)} = 180\). In the right triangle: \(A+66 + x=180\).
Subtract the two equations: \((A + 68+\text{angle1})-(A + 66+x)=0\). But since \(\text{angle1}\) and \(x\) are related through the vertical - angle equality.
The better way is:
Since the sum of angles in a triangle is \(180^{\circ}\).
For the left - hand side triangle (with \(68^{\circ}\) angle) and the right - hand side triangle (with \(66^{\circ}\) and \(x\) angles), because of vertical angles (equal), we have \(68+66 + x=180\) (by equating the sum of angles in the two triangles considering the vertical - angle equality).

$$x=180-(68 + 66)$$

$$x=180 - 134$$

$$x = 46$$

Answer:

\(46\)