Question

1. use the diagram to solve for x: 64° 116° 58° 26°

Explanation:

Step1: Use the property of adjacent angles on a straight line

The sum of adjacent angles on a straight line is \(180^{\circ}\). But here, we can use the property of parallel lines and transversal. The angle \(116^{\circ}\) and \(x\) are not adjacent in the sense of a straight - line sum. Instead, we use the property that when two parallel lines are cut by a transversal, the sum of an interior angle and its adjacent exterior - like angle (in the non - straight - line adjacent pair for the purpose of parallel lines) is not relevant here. Wait, no. Actually, when two parallel lines are cut by a transversal, the sum of a pair of same - side interior angles is \(180^{\circ}\). But no, looking at the diagram (assuming the two lines with blue arrows are parallel), the angle \(116^{\circ}\) and \(x\) are not same - side interior. Wait, no, actually, if we consider the linear - pair property (but in the context of parallel lines, we can also use the fact that the angle adjacent to \(116^{\circ}\) (let's call it \(y\)) forms a linear pair (\(y + 116^{\circ}=180^{\circ}\), so \(y = 64^{\circ}\)), and then using the property of alternate interior angles (if the lines are parallel), but no, actually, if we consider the transversal and the two parallel lines, the angle \(x\) and the angle adjacent to \(116^{\circ}\) (calculated as \(180 - 116=64^{\circ}\)) are corresponding angles (assuming the correct orientation of parallel lines and transversal). But wait, another approach:
We know that the sum of angles on a straight line is \(180^{\circ}\). If we assume the two lines with blue arrows are parallel and the transversal cuts them. The angle \(116^{\circ}\) and \(x\) are not in a straight - line adjacent pair for the parallel - line - transversal system in the wrong way. Wait, no, actually, if we consider the fact that the angle adjacent to \(116^{\circ}\) (let \(a\) be the adjacent angle, \(a + 116^{\circ}=180^{\circ}\), so \(a = 64^{\circ}\)), and if the lines are parallel, then \(x=a\) (corresponding angles).

Step2: Calculate \(x\)

Since \(x + 116^{\circ}=180^{\circ}\) (this is wrong, wait no. Wait, no, the correct formula is: If we consider the angle adjacent to \(116^{\circ}\) (let's call it \(z\)), \(z=180 - 116\). And if the lines are parallel, \(x = z\) (corresponding angles). So \(x=180 - 116\)

$$x=64^{\circ}$$

Answer:

\(64^{\circ}\)