Question

find the measure of the \?\ or \x\.

Explanation:

Step1: Use the property of vertical - angle equality

Vertical angles are equal. Let's assume the two triangles have vertical - angle equality.

Step2: Apply the triangle - angle - sum theorem

The sum of angles in a triangle is \(180^{\circ}\).
For the first triangle with angles \(35^{\circ}\), \(?\), and the vertical - angle. For the second triangle with angles \(54^{\circ}\), \(30^{\circ}\), and the vertical - angle.
Since the vertical - angle is common, we have \(35^{\circ}+?=54^{\circ}+30^{\circ}\) (because the sum of the non - vertical angles in each of the two triangles (with the vertical - angle) must be equal as the sum of angles in a triangle is \(180^{\circ}\)).

Step3: Solve for the unknown angle

$$
LATEXBLOCK0
$$

Answer:

\(49^{\circ}\)