Question

what is the value of x? input box find the measure of angle 1. input box skill code: 1062113 (diagram with intersecting lines, angles labeled 118°, 6x + 4, and angle numbers 1, 3, 4, 5, 7, 8)

Explanation:

Step1: Identify equal angles

The angle with measure \(118^\circ\) and the angle labeled \(6x + 4\) are corresponding angles (since the lines are parallel, as indicated by the arrow marks), so they are equal. Thus, we set up the equation:
\(6x + 4 = 118\)

Step2: Solve for \(x\)

Subtract 4 from both sides:
\(6x + 4 - 4 = 118 - 4\)
\(6x = 114\)
Divide both sides by 6:
\(x = \frac{114}{6}\)
\(x = 19\)

Step3: Find measure of angle 1

Angle 1 and the angle \(6x + 4\) are supplementary (they form a linear pair). First, find \(6x + 4\) when \(x = 19\):
\(6(19) + 4 = 114 + 4 = 118\)
Then, angle 1 is \(180^\circ - 118^\circ = 62^\circ\) (or, since angle 1 and the angle adjacent to \(118^\circ\) are equal, we could also note that vertical angles or corresponding angles might apply, but the linear pair is straightforward here).

Answer:

Value of \(x\): \(19\)
Measure of angle 1: \(62^\circ\)