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 measure of the missing angle is □°. the figure is not drawn to scale. help me solve this view an example get more help - clear all

Explanation:

Step1: Recall angle - sum property of a triangle

The sum of the interior angles of a triangle is 180°.

Step2: Consider the top - triangle

Let the unknown angle in the top - triangle be \(x\). In the top - triangle, we know one angle is 64°. In the bottom - triangle, the angle opposite to the 61° angle (vertically opposite angles are equal) is also 61°.
For the top - triangle, using the angle - sum property of a triangle \(180^{\circ}=64^{\circ}+x + 61^{\circ}\).

Step3: Solve for \(x\)

We can rewrite the equation as \(x=180^{\circ}-(64^{\circ}+61^{\circ})\).
First, calculate the sum inside the parentheses: \(64^{\circ}+61^{\circ}=125^{\circ}\).
Then, \(x = 180^{\circ}-125^{\circ}=55^{\circ}\).

Answer:

55