Question

a company is making different size statues that are in the shape of glasses. use the figure to find the missing measure, $x^{circ}$. the figure is not drawn to scale. a 55 b 45 c 40 d 50

Explanation:

Step1: Recall angle - equality property

The two vertical angles in the figure are equal. Let the vertical - angle pair be equal.

Step2: Use angle - sum property of a triangle

For the upper triangle, the sum of interior angles of a triangle is 180°. So, \(64^{\circ}+x^{\circ}+\text{(vertical angle)} = 180^{\circ}\). Since the vertical angle is equal to the 70° angle in the lower triangle, we have the equation \(64 + x+70=180\).

Step3: Solve for \(x\)

First, simplify the left - hand side of the equation: \(64 + 70+x=134 + x\). Then, set up the equation \(134+x = 180\). Subtract 134 from both sides: \(x=180 - 134\). So, \(x = 46\).

Answer:

B. 46