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, $x^{circ}$. the measure of the missing angle is $square^{circ}$. the figure is not drawn to scale.

Explanation:

Step1: Use the triangle angle - sum property

The sum of angles in a triangle is \(180^{\circ}\). For the lower triangle, if one angle is \(61^{\circ}\), and for the upper triangle, the non - \(65^{\circ}\) and non - \(x^{\circ}\) angle is equal to the angle in the lower triangle (vertically opposite angles are equal).
Let the common angle (vertically opposite angles) be \(y\). So, \(y = 61^{\circ}\) (vertically opposite angles).
For the upper triangle, using the angle - sum property of a triangle: \(65^{\circ}+x^{\circ}+y^{\circ}=180^{\circ}\).
Substitute \(y = 61^{\circ}\) into the equation: \(65 + x+61=180\).

Step2: Solve for \(x\)

Simplify the left - hand side of the equation: \(x+126 = 180\).
Subtract 126 from both sides: \(x=180 - 126\).

Answer:

\(54\)